ORIGINAL CONTRIBUTION

Structure and dynamics of dextran in binary mixturesof a good and a bad solvent

Eleftheria Antoniou & Efrosyni Themistou &

Biswajit Sarkar & Marina Tsianou &

Paschalis Alexandridis

Received: 31 March 2010 /Revised: 29 June 2010 /Accepted: 30 June 2010 /Published online: 17 July 2010# Springer-Verlag 2010

Abstract The structure and dynamics of the commonpolysaccharide dextran have been investigated in mixedsolvents at two different temperatures using small-angleX-ray scattering (SAXS) and viscosity measurements. Morespecifically, binary mixtures of a good solvent (water,formamide, dimethylsulfoxide, ethanolamine) and the badsolvent ethanol as the minority component have been con-sidered. The experimentally observed effects on thepolymer conformation (intrinsic viscosity, coil radius, andradius of gyration) of the bad solvent addition are discussedin terms of hydrogen bonding density and are correlatedwith the Hansen solubility parameters and the surfacetension of the solvent mixtures. Hydrogen bonding appearsto be an important contributor to the solubility of dextranbut is not sufficient to capture the dextran coil contractionin the mixtures of good+bad solvents.

Keywords Polymer . Solvent . Viscosity . Dextran .

Scattering

Introduction

The development of new, complex materials inspired bynature or driven by human needs is of great importance intoday’s materials science. Information and understanding ofthe material structure, processing, and properties are neededto this end. This is especially true for novel polymer-based

materials. In addition to the widespread traditional uses ofpolymers, rapid advances take place in novel applicationssuch as optoelectronics [1]. At the same time, fundamentalknowledge of structure–property relationships of polymericfluids is important for the understanding of biologicalsystems containing biopolymers such as DNA and proteins[2, 3].

Polymers can exhibit a rich behavior in the presence ofsolvents. In dilute solution, the polymer conformationdepends mainly on the interactions between the polymerchain segments and the solvent molecules [4, 5]. Polymercoils can expand or contract from their unperturbeddimensions depending on the quality of the solvent theyare dissolved into. A solvent can be good (the number ofsolvent–segment contacts is maximized and the polymercoil expands), bad (the polymer coil contracts in order tominimize the segment–solvent interactions), or theta (un-perturbed coil dimensions). The solvent quality and, as aresult, the polymer conformation can be tuned by theaddition of cosolvents. This is common for water-solublepolymers and particularly important for the pharmaceuticalindustry, where many actives and excipients do not dissolvewell in aqueous solutions, and for the coatings and paintsindustries which are subject to environmental regulations asto the type and amount of organic solvents present in theformulation [6, 7].

The structure and properties of polymers in single andmixed solvents have been of great interest to our group [8–13]. We have recently investigated the solution behavior ofa water-soluble polysaccharide, dextran, in single and inmixed solvents using viscometry [14, 15]. Dextran findsseveral applications (e.g., in several consumer products [16,17] and as a plasma volume expander in clinical applica-tions [18, 19]) and has been previously studied in singlesolvents [20, 21] but, to the best of our knowledge, never in

E. Antoniou : E. Themistou :B. Sarkar :M. Tsianou (*) :P. Alexandridis (*)Department of Chemical and Biological Engineering, Universityat Buffalo—The State University of New York (SUNY),Buffalo, NY 14260-4200, USAe-mail: mtsianou@buffalo.edue-mail: palexand@buffalo.edu

Colloid Polym Sci (2010) 288:1301–1312DOI 10.1007/s00396-010-2259-x

solvent mixtures until our recent report on binary mixturesof good solvents [15].

Here, we consider dextran dissolved in binary solventmixtures consisting of a good and a bad solvent; wefocus on “how” the polymer conformation responds tochanges in the solvent quality and address the “why” onthe basis of polymer–solvent interactions. We areinterested in the physicochemical properties involvingsolute–solvent interactions in mixed solvents in view oftheir greater complexity in comparison with pure sol-vents [6, 22]. Both macroscopic (viscosity) and micro-scopic (SAXS) data are analyzed in terms of the polymerconformation for binary mixtures of ethanol (non-solventfor dextran) and one of the following good solvents (inorder of increasing solvent quality): water, formamide,dimethylsulfoxide, and ethanolamine. All these solventsare relevant to a range of applications. For example,amide-containing multi-component solvent systems arecommonly used in chemical reactions and industrialprocesses and are interesting for the study of peptide andprotein interactions in biological systems [23]. Thedextran coil radius data are evaluated for possiblecorrelations with properties of the mixed solvents suchas the fractional solubility parameters and surface tension.While some studies have attempted to correlate dextransolution behavior to solvent properties in single solvents[24], there are no such studies in mixed solvents. Theunderlying polymer–solvent interactions that emerge fromsuch analysis are corroborated by data collected at twodifferent temperatures.

Materials and methods

Materials

We consider here the T500 dextran fraction, with weightaverage (Mw) and number average (Mn) molecular weights500,000 and 191,500, respectively, purchased from Amer-sham Biosciences AB (now part of GE Healthcare,Uppsala, Sweden) and Pharmcosmos A/S (Holbaek, Den-mark). Ethanolamine (purified grade, 99% min) wasobtained from Fisher Scientific (Fair Lawn, NJ, USA).Formamide (molecular biology grade) was purchased fromVWR International (West Chester, PA, USA), dimethylsulf-oxide (DMSO) from Fisher Scientific (Fair Lawn, NJ,USA), and ethanol from Decon Labs, Inc. (King of Prussia,PA, USA). The water used was purified with a Milli-Qsystem.

Given volumes of two solvents were mixed to create amixed solvent of desired composition. Samples wereprepared individually for every dextran concentration bydissolving the appropriate amount of polymer in a given

mixed solvent. The samples remained under stirring for atleast 1 day at room temperature and then equilibrated at 20or 40 °C for at least an hour before the measurements wereconducted at the same temperature.

Methods

We performed viscosity measurements at both 20 and 40 °Cfor dextran T500 in mixtures of water, formamide,DMSO, or ethanolamine (all good solvents for dextran)with ethanol (non-solvent for dextran). The viscosity ofdilute dextran solutions was determined using CannonFenske Routine-type viscometers [25] for transparentNewtonian fluids (dextran solutions exhibit Newtonianflow characteristics according to [26]). Different sizes ofviscometers were used depending on the viscosity range ofthe samples. The viscometer was placed inside a constanttemperature bath to ensure that the measurements were takenunder constant temperature (controlled to within ±0.1 °C).The efflux times were reproducible to ±0.1% (each measure-ment was repeated three times) and were measured with anaccuracy of ±0.1 s. The kinematic viscosity η is calculated bymultiplying the efflux time with the viscometer calibrationconstant (supplied by the manufacturer Cannon InstrumentCo., State College, PA, USA). The viscosity data analysisprocedure has been presented previously [27]. Briefly,focusing on data in the dilute regime, we obtain the intrinsicviscosity for dextran, and then we extract the coil dimensions(see below).

Intrinsic viscosity

The intrinsic viscosity values, [η], of dextran in differentsolvents and at different temperatures are determined usingthe Huggins (1) and Kramer (2) equations [5, 28] byplotting ηsp/C and ln(ηrel)/C, respectively, against thepolymer concentration, and subsequently extrapolating tozero polymer concentration (infinite dilution) (Fig. 1).

hsp=C ¼ h½ � þ k 0 h½ �2C ð1Þ

lnhrelð Þ=C ¼ h½ � � k 00 h½ �2C ð2Þηrel is the relative viscosity (hrel ¼ h=h0, η and η0 are the

kinematic viscosity of the solution and the pure solvent,respectively), ηsp is the specific viscosity (hsp ¼ hrel � 1),k′ and k″ are the Huggins and Kramer constants, respec-tively, and C is the concentration (g/dl) of the polymersolution. A straight line is obtained when the data areplotted according to Eqs. 1 and 2, with [η] being theintercept (see Fig. 1). The [η] values extracted from ourexperiments are presented in Table 1. We estimate the [η]

1302 Colloid Polym Sci (2010) 288:1301–1312

error at ±4.7%. These error bars signify the ±2σ range ofthe measurements, where σ denotes the [η] uncertainty thatcorresponds to the 95% confidence interval. In order toestimate σ, we followed both an analytical and a numericalapproach. For the first case, the uncertainty of theviscosity measurements was propagated to the internalviscosity using the standard first-order Taylor expansionof the uncertainty expression [29]. All intermediate stepoperations were taken into account. For the latter case, weused a Monte Carlo simulation. A very large number ofrandom viscosity values were drawn from the viscositymeasurements distribution, and for each sample theinternal viscosity was obtained following the standardforward calculation. σ was estimated from the resultinginternal viscosity distribution. The uncertainty valuesobtained by both approaches turned out to be almostidentical.

Hydrodynamic coil radius

The increase in viscosity of a dilute dispersion of uniform,rigid non-interacting spheres can be expressed by theEinstein viscosity relation (Eq. 3) [25]:

h ¼ h0 1þ 2:5Φð Þ ð3Þwhere Φ is the volume fraction of the spheres in thesolution. Starting from Eq. 3, we derive an equation todetermine the hydrodynamic coil radius, Rcoil [27]:

Rcoil ¼ 3½ ½h� �Mw=10p � NAV�1=3 cmð Þ ð4ÞwhereMw is the polymer weight average molecular weight andNAV is Avogadro’s number. The Rcoil and the correspondinghydrodynamic coil volume, Vcoilð¼ ð4=3ÞpRcoil

3Þ, values fordextran T500 in different solvent systems are reported inTable 1. We estimate the Rcoil error at ±1.6%.

Overlap concentration

The overlap concentration, C*, marks the crossoverbetween the dilute regime and the concentration regimewhere polymer coils overlap [30]. C* may be betterrepresented by a concentration range rather than by a singleconcentration value. Having said this, a single value for C*renders comparisons easy to make. To this end, we used [η]to estimate C* according to Eq. 5 [31]. The C* values thusobtained are given in Table 1.

C» ¼ 2:5= h½ � ð5Þ

Voluminosity and shape factor of the polymer coil

The voluminosity (VE) is a measure of volume of a solvatedpolymer molecule; thus, it conveys information regardingthe polymer conformation in different solvent conditions.The relative viscosity data can be used to calculate thevoluminosity of the polymer solution by plotting Y (asdefined below) against C [32]:

Y¼ h0:5rel � 1� �

= C 1:35h0:5rel � 0:1� �� � ð6Þ

VE for different solvent conditions can be obtained fromthe intercept at C=0 of the line going through the Y vs. Cdata. Values of voluminosity of dextran T500 polymer coilsin the different solvents considered here were calculatedusing Eq. 6 and are presented in Table 2.

The intrinsic viscosity and VE are related through thefollowing relation [32]:

h½ � ¼ n VE ð7Þwhere ν is the shape factor that gives an idea about theshape of the particles in solution. A value of 2.5 for ν

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

n sp/

c (d

l/g)

and

ln(η

rel)/

c

C (g/dl)

Water

Formamide

Ethanolamine

DMSO

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

n sp/

c (d

l/g)

and

ln(η

rel)/

c

C (g/dl)

Water

Formamide

Ethanolamine

DMSO

a

b

Fig. 1 Specific viscosity (filled symbols) and logarithm of relativeviscosity over concentration (open symbols) plotted and linearly fittedversus concentration, C, of dextran T500 in mixtures of thegood solvent ethanolamine (diamond), formamide (triangle), DMSO(circle), or water (square) with the bad solvent ethanol (25% v/v) ata 20 °C and b 40 °C

Colloid Polym Sci (2010) 288:1301–1312 1303

suggests that the particles (in this case, polymer coils) arespherical in nature [32]. Values of ν higher than 2.5 indicateellipsoidal particles. The shape factors of dextran T500calculated from Eq. 7 are very close to 2.5 (see Table 2),consistent with polymer coils in all the different solvent andtemperature conditions examined here.

Small-angle X-ray scattering

Small-angle scattering has proven an important methodfor the characterization of macromolecular structure insolution [5, 33]. We carried out small-angle X-ray (SAXS)measurements of 1 wt.% dextran T500 solutions with aNano-STAR instrument (Bruker-AXS, Madison, WI,USA). The concentration used was below the overlapconcentration. The scattering intensity, I(q), at wave vectorq is proportional to the form factor P(θ). We considered

the fit to the SAXS data of the random coil form factor,P(θ):

P qð Þ ¼ 2=x2� �

e�x � 1� xð Þ½ �;where x ¼ qRg

� �2 ð8Þ

The coil radius of gyration, Rg, is the main fittingparameter. In addition to Rg, a scale factor and a (constant)background term are involved in the data fitting.

In Fig. 2 the X-ray scattering intensity, I(q), is plottedagainst q for the case of dextran T500 in water, formamide,ethanolamine, and their mixtures with 25% ethanol. Datafits using the random coil form factor P(θ) are also shown.Dextran behaves as random coil in water, formamide, andethanolamine solutions at room temperature, since the datain all cases are adequately fitted by the random coil formfactor. These SAXS data are important in establishing thedextran conformation in solution since this technique is a

20°C 40°C

0vol.% ethanol 25vol.% ethanol 0vol.% ethanol 25vol.% ethanol

VE ν VE ν VE ν VE ν(dl/g) (dl/g) (dl/g) (dl/g)

Ethanolamine 0.366 2.63 0.261 2.45 0.337 2.54 0.221 2.51

DMSO 0.317 2.49 0.167 2.51 0.297 2.49 0.145 2.53

Formamide 0.266 2.51 0.192 2.46 0.237 2.49 0.181 2.51

Water 0.197 2.50 0.131 2.50 0.184 2.48 0.1290 2.50

Table 2 Effect of ethanol onvoluminosity (VE) and shapefactor (ν) in different single andbinary good+bad solvents at 20and 40 °C

Table 1 Intrinsic viscosity [η], hydrodynamic coil radius Rcoil, hydrodynamic coil volume Vcoil, and overlap concentration C*, for dextran T500in single and binary good+bad solvents, calculated using the viscosimetric data obtained in this work at 20 and 40 °C

Solvent volume % Mole % 20°C 40°C

[η](dl/g)

Rcoil

(nm)Vcoil

(103nm3)C*(g/dl)

[η](dl/g)

Rcoil

(nm)Vcoil

(103nm3)C*(g/dl)

100% ethanolamine 100% 0.964 19.7 32.0 2.6 0.854 18.9 28.3 2.9

75% ethanolamine/25% ethanol 76%/24% 0.640 17.2 21.3 3.9 0.554 16.4 18.4 4.5

65% ethanolamine/35% ethanol 66%/34% 0.429 15.0 14.1 5.8

100% DMSO 100% 0.792 18.5 26.3 3.2 0.742 18.1 24.8 3.4

75% DMSO/25% ethanol 71%/29% 0.420 14.9 13.8 5.9 0.367 14.3 12.2 6.8

100% formamide 100% 0.669 17.4 22.1 3.7 0.591 16.7 19.5 4.2

85% formamide/15% ethanol 88%/12% 0.545 16.3 18.1 4.6

75% formamide/25% ethanol 80%/20% 0.472 15.5 15.7 5.3 0.454 15.3 15.0 5.5

100% water 100% 0.491 15.7 16.2 5.1 0.457 15.4 15.3 5.5

85% water/15% ethanol 95%/5% 0.405 14.8 13.6 6.2 0.394 14.6 13.0 6.4

75% water/25% ethanol 91%/9% 0.327 13.7 10.8 7.7 0.322 13.7 10.8 7.8

70% water/30% ethanol 88%/12% 0.285 13.1 9.4 8.8

1304 Colloid Polym Sci (2010) 288:1301–1312

direct probe of the structure (whereas viscosity is indirect).The Rg values follow the same trends as the Rcoil values, butfor a given solvent the two radii differ somewhat (seeTable 3). In what follows, we focus our discussion on theRcoil data which constitute a more extensive data set andone that is directly comparable to data that we hadpreviously obtained for dextran in single solvents.

Results and discussion

We consider here mixtures of a good and a bad solvent inorder to investigate how the solvent quality decreases uponthe addition of a bad solvent. In particular we presentinformation on dextran dissolved in binary mixtures of agood solvent (water, formamide, dimethylsulfoxide, orethanolamine) and a bad solvent (ethanol) as a minorcomponent, as affected by temperature. Dextran adopts arandom coil conformation in water and in single polarorganic solvents such as formamide and ethanolamine, asattested to by analysis of viscosity data reported previously[14, 27] and the small-angle X-ray scattering data presentedhere (Fig. 2). The magnitude of the intrinsic viscosity, [η],can be considered as a measure of solvent quality: thegreater the [η], the better the solvent. The coil radius, Rcoil,in the solvent systems used in this work has been calculatedthrough [η], using Eq. 4. Below, we discuss the solvent andtemperature effects in terms of the dextran coil dimensions,Rcoil.

The dextran T500 [η] and Rcoil, reflective of conformation,in the four binary solvent systems of water, formamide,dimethylsulfoxide, or ethanolamine mixed with ethanol (badsolvent) as minor component are presented in Table 1 and inFigs. 3 and 4, plotted against the ethanol content (vol.% ormol%) in the mixture. In all cases, the dextran coil radii (andvolume) decreased upon ethanol addition (see Table 1 andFigs. 3 and 4), and C* increased (Table 1). The decrease inthe dextran coil dimensions is also supported by the Rg datafrom SAXS (Table 3). At 20 °C, the Rcoil drop caused by 25v/v % ethanol was approximately 20% in the DMSO/ethanol

0.001

0.01

0.1

0.01 0.1

I exp - WaterI theor- waterI exp- water-EtOHI theo- water-EtOH

I (cm

-1)

q (A-1)

Water

0.001

0.01

0.1

0.01 0.1

I exp - FormamideI theor- formamideI exp- form-EtOHI theo- form-EtOH

I (cm

-1)

q (A-1)

Water

0.001

0.01

0.1

0.01 0.1

I exp - EthanolamineI theor- EthanolamineI exp- Ethanolamine-EtOHI theo- Ethanolamine-EtOH

I (cm

-1)

q (A-1)

Water

a

b

c

Fig. 2 Small-angle X-ray scattering intensity (I) versus scatteringvector (q) data for 1 wt.% dextran T500 in a aqueous and water +25%ethanol solutions, b formamide and formamide + 25% ethanolsolutions, and c ethanolamine and ethanolamine + 25% ethanolsolutions (open square, single solvents; open circle, mixed solvents;solid lines, random coil fits)

Table 3 Radius of gyration, Rg, obtained from SAXS data, and coilradius, Rcoil, obtained from viscosity data for dextran T500 in singleand binary good+bad solvents (20 °C)

Solvent (vol.%) Rg (nm) Rcoil (nm)

100% ethanolamine 17.5 19.7

75% ethanolamine/25% ethanol 12.8 17.2

100% formamide 20.0 17.4

75% formamide/25% ethanol 14.0 15.5

100% water 19.8 15.7

75% water/25% ethanol 16.0 13.7

Colloid Polym Sci (2010) 288:1301–1312 1305

mixed solvent, 13% in water/ethanol and ethanolamine/ethanol, and 11% in formamide/ethanol. The change in theRg values upon 25% v/v ethanol addition was approximately30% for the formamide and ethanolamine cases and 20% inthe aqueous mixture. The Rg % changes are higher thanthose observed for Rcoil. The introduction of ethanol alsoresulted in a decrease of the dextran voluminosity (Table 2),indicating a reduction in the solvation of the dextranmolecules. Clearly, the solvent power of ethanolamine,DMSO, formamide, and water decreased upon addition ofethanol. In the case of dextran dissolved in single solvents,we found the ability of a solvent to increase [η] and expandthe coils to increase in the order: water < formamide <dimethylsulfoxide < ethanolamine [14]. This order appearsto be retained in binary mixtures of these solvents withethanol, although the relative position of formamide anddimethylsulfoxide switches at more than 20v/v% ethanol.

When ethanol is measured in volume percent, itexhibits a more pronounced effect (as judged by theslope of the lines in Fig. 3) when added to DMSOcompared to the other solvents. However, in terms of molepercent, the addition of ethanol has a greater effect ondextran in aqueous solutions (Fig. 4). Only 4.5 mol%ethanol needs to be added to the aqueous dextran solutionin order to cause a 5% decrease in the dextran Rcoil,whereas 7.5, 9.6, and 9.9 mol% ethanol is necessary inDMSO, ethanolamine, and formamide, respectively, toeffect the same 5% Rcoil decrease.

As the temperature increased from 20o to 40 °C, thedextran coil dimensions decrease (see Table 1), with theethanolamine, DMSO, and formamide–ethanol mixedsolvent systems being more affected (up to 14%) and theaqueous ethanol mixtures less (0–6%), indicating that thesolvent power of all the mixed solvents decreases. This isconsistent with the low critical solution temperature(LCST) behavior. As temperature increases, LCST poly-mers contract towards their unperturbed dimensions,where the polymer coil size reflects only its ownmolecular conformational constraints (and is not swollenby the solvent) [5]. A temperature increase from 20 to 40 °C decreased the dextran Rcoil in water from 15.7 to15.4 nm, moving it closer to its unperturbed coildimension in water (14.9 nm at 43 °C [21]), whereas theaddition of 25% ethanol to water moved the dextran Rcoil

to 13.7 nm, a value lower than its unperturbed coildimensions in water. In the case of DMSO (where theunperturbed coil dimension of dextran is 16 nm at 45 °C[34]), a temperature increase from 20 to 40 °C decreasedthe dextran Rcoil from 18.5 to 18.1 nm, while ethanoladdition contracted Rcoil down to 14.9 nm, lower than theunperturbed coil dimension of dextran in DMSO, butwithout any apparent signs of phase separation (cloudpoint). The effect of temperature increase on the dextran

12

13

14

15

16

17

18

19

20

0% 10% 20% 30% 40% 50%

Rco

il (n

m)

ethanol mole%

20oCWater

Formamide

Ethanolamine

Dimethylsulfoxide

Fig. 4 Coil radius, Rcoil, of dextran T500 in mixtures of the goodsolvent water (open square), formamide (open circle), dimethylsulf-oxide (open diamond), and ethanolamine (open triangle) with the badsolvent ethanol plotted vs. the ethanol content (mol%) at 20 °C

0

0.2

0.4

0.6

0.8

1

0% 10% 20% 30% 40% 50%

[η] (

dl/g

)

ethanol v/v%

20 C

Water

Formamide

Ethanolamine

Dimethylsulfoxide

12

13

14

15

16

17

18

19

20

0% 10% 20% 30% 40% 50%

Rco

il (n

m)

ethanol v/v%

20 CWater

Formamide

Ethanolamine

Dimethylsulfoxide

a

b

Fig. 3 a Intrinsic viscosity, [η], and b coil radius, Rcoil, of dextranT500 in mixtures of the good solvent water (open square), formamide(open circle), dimethylsulfoxide (open diamond), and ethanolamine(open triangle) with the bad solvent ethanol plotted vs. the ethanolcontent (% v/v) at 20 °C

1306 Colloid Polym Sci (2010) 288:1301–1312

coil dimensions is thus less pronounced than the effect ofethanol addition.

The voluminosity of the dextran coils also decreasedupon heating in all the solvents examined, reflecting aworsening of the solvent quality at elevated temperature. Asimilar decrease in voluminosity at elevated temperaturehas been reported for acrylonitrile–acrylate copolymers indimethylformamide [32]. The degree of voluminositychanges due to a given temperature change appearingdifferent for different solvents: higher in the case ofethanolamine and DMSO and their mixtures with ethanol,and lower in formamide and water. Overall, the effect oftemperature on voluminosity is not as strong as that ofethanol addition.

In what follows, we attempt to explain the observedchanges in the dextran coil dimensions in mixed solvents interms of interactions between solvent molecules andpolymer segments. We first invoke the number ofhydrogen-bonding sites available per unit volume. We thenexamine possible correlations of the coil dimensions ofdextran to properties of the mixed solvent system such asfractional solubility parameters and surface tension.

Hydrogen bond density

We would expect that the hydrogen bond density can be avalid indicator of dextran solvation, on the basis of previousstudies [14, 15]. As shown in Table 4, the H bond densityneeded to effect a 5% change of Rcoil is 28 H bond sites/nm3, approximately the same for ethanol mixtures informamide, ethanolamine, and DMSO. Let us now considerinteractions between the two solvents (in the absence ofdextran) in order to rationalize the significance of thisobservation. We note that available literature on interactionsin binary solvent mixtures is very limited. DMSO formscomplexes with proton donors (three to four H bonds permolecule) using the oxygen atom of the S = O group [35].Ethanol has one –OH group that interacts with DMSOthrough H bonding [35]. So, when dextran molecules aredissolved in the DMSO–ethanol mixture, they interact withfewer DMSO H bonding sites than when in pure DMSO.The solvent quality thus decreases compared to pure DMSOand the dextran Rcoil contracts. The same is observed in thecase of dextran in formamide–ethanol mixtures: formamide

and ethanol interact through H bonding [23] causing adecrease in the H bonding sites available to interact withdextran.

Regarding the water–ethanol mixed solvent, a 5% Rcoil

decrease corresponds to a decrease from 66 H-bond sites/nm3 in pure water to 58 in 15v/v% ethanol (see Table 4).Even though 58 is almost double the H bond density in theethanol mixtures with ethanolamine, formamide, or DMSO,still the dextran Rcoil exhibits its smallest value in the water-ethanol mixture. In the case of ethanol in water (atconcentrations below 0.18 molar fraction or 42v/v%ethanol), clusters form between ethanol and water mole-cules, and the arrangement of water molecules becomesmore ordered [36]. This structural enhancement of thealready very dense H-bonded network of water allowsdextran few sites to interact with and makes it moredifficult for dextran coils to swell with solvent, thus thesolvent quality of water decreases significantly.

Temperature dependence studies on water and polarsolvents like formamide [37, 38] indicate that the structureof these solvents is not affected significantly by tempera-ture. It is rather the hydrogen bonding stability that isinfluenced (i.e., it decreases as temperature increases). Thecontraction of the dextran coils that we observe uponheating can be attributed to a decrease of the stability of thehydrogen bonds between dextran and solvent molecules[15, 21] and a relative increase of the stability ofintramolecular interactions among the polymer segmentsof dextran.

Fractional solubility parameters

The Hildebrand solubility parameter of a given (single)solvent, δ, can be attributed to three distinct contributions:δD (due to dispersion forces), δP (due to polar dipole–dipoleforces), and δH (due to hydrogen bonding) [39] according toEq. 9:

d2 ¼ dD2 þ dP

2 þ dH2 ð9Þ

The relative importance of the three component forces(dispersion, polar, and hydrogen bonding) can be expressedin terms of the fractional solubility parameters (FSPs), fD,fP, and fH, obtained from Eq. 10 [30]. The sum of fD, fP, and

Solvent Vm 103nm3/molecule HB/molecule HB/nm3 HB/nm3 (5% Rcoil decrease)

Ethanolamine 99 2 (OH, NH3) 30.22 28 (10% v/v EtOH)

Formamide 66 2 (CO, NH3) 30.27 28 (12.5% v/v EtOH)

Dimethylsulfoxide 118 4 (S=O) 33.79 32 (6.25% v/v EtOH)

Water 30 2 (H, OH) 66.92 58 (15% v/v EtOH)

Ethanol 97 1 (OH) 10.30 –

Table 4 Molecular volume,number of hydrogen bonds(HB) per molecule, and numberof HB/nm3, of the single sol-vents used in this study; numberof HB/nm3 present in theirbinary mixtures with ethanol, atethanol content such that causeda 5% coil radius decrease

Colloid Polym Sci (2010) 288:1301–1312 1307

fH is 100. FSPs of mixed solvents are determined bycalculating the volume-wise contributions of the solubilityparameters of the individual components of the mixture(δ and f values are reported in Table 5).

fD ¼ 100 dD= dD þ dP þ dHð ÞfP ¼ 100 dP= dD þ dP þ dHð ÞfH ¼ 100 dH=ðdD þ dP þ dHÞ

ð10Þ

Polymers tend to dissolve in solvents that have similarsolubility parameters [39]. A ternary diagram (Teas graph)that presents all three FSPs in a two-dimensional plot andallows visualization of the solubility parameter space isshown in Fig. 5 for mixtures of ethanol with water,formamide, DMSO, or ethanolamine. The FSP values ofpure formamide and DMSO are rather close to those ofdextran. The FSP values of formamide or DMSO mixtureswith ethanol move closer to the FSP values of dextran asthe ethanol content increases toward 100% ethanol. In thecase of ethanolamine, its FSP values are very close to thoseof dextran and move away with an ethanol content increase.The FSP values of water and its mixtures with ethanol arerather different than those of dextran. We can identify inFig. 5 a range of FSP values where relatively good solventsfor dextran can be found. The location of this range withrespect to the apexes of the ternary diagram points to thehigher relative importance in dextran solubility of the polar,fP, and the hydrogen bonding, fH, fractional solubilityparameters over the dispersion parameter, fD. The solventsystems (e.g., ethanol) that fall outside this range arerelatively bad solvents for dextran.

While Fig. 5 compares the FSPs of the solvent mixturesto those of dextran, the possible impact of the solvent FSPsto the dextran Rcoil can be revealed in Fig. 6, where the coilradius of dextran is plotted as a function of the FSPs ofeach of the different mixed solvent systems used in this

work. Focusing on fP that emerged as relatively moreimportant from Fig. 5, we can see that, in all casespresented in Fig. 6, the Rcoil of dextran decreased as fPdecreased toward the value for pure ethanol. A decrease inRcoil can be further associated with an increase in fH. Thus,a relative increase of the H bonding contribution to thesolvent cohesive forces compared to polar force contribu-tion renders more difficult for dextran to disrupt the solventH bonds and less likely to swell with the solvent.

In Fig. 7, we present the dextran Rcoil data for all themixed solvents studied here plotted against each of the

Solvent δ δD δP δH fD fP fH

100% ethanolamine 31.3 17.0 15.5 21.2 31.6 28.9 39.5

75% ethanolamine/25% ethanol – – – – 32.7 26.7 40.6

65% ethanolamine/35% ethanol – – – – 33.2 25.8 41.1

100% DMSO 26.7 18.4 16.4 10.2 40.9 36.4 22.7

75% DMSO/25% ethanol – – – – 39.7 32.3 28.0

100% formamide 36.7 17.2 26.2 19.0 27.6 42.0 30.4

85% formamide/15% ethanol – – – – 28.8 38.7 32.5

75% formamide/25% ethanol – – – – 29.6 36.5 33.9

100% water 47.8 15.5 16.0 42.3 21.0 21.7 57.3

85% water/15% ethanol – – – – 23.2 21.5 55.3

75% water/25% ethanol – – – – 24.7 21.3 54.0

70% water/30% ethanol – – – – 25.5 21.2 53.3

100% ethanol 26.5 15.8 8.8 19.4 35.9 20.0 44.1

Dextran 38.6 24.3 19.9 22.5 36.5 29.8 33.7

Table 5 Hildebrand (δ) andHansen (δD, δP, δH) solubilityparameters (in units of MPa1/2)of the single solvents and frac-tional solubility parameters (fD,fP, fH) of the single solvents,binary solvent mixtures, andpolymer used in this study. Thereported solvent compositionsare in volume percent

fD0 10 20 30 40 50 60 70 80 90 100

fP

0

10

20

30

40

50

60

70

80

90

100

fH

0

10

20

30

40

50

60

70

80

90

100

Dextran

100% Ethanol100% Water

100% EthanolamineEthanolamine/25%EtOH

100% FormamideFormamide/ 15% EtOH

Ethanolamine/35%EtOH

Formamide/ 25% EtOHDimethylsulfoxide/ 25% EtOH

100% Dimethylsulfoxide

Fig. 5 Teas graph of the three fractional solubility parameters fD, fP, fHof mixtures of the good solvents ethanolamine (open triangle),dimethylsulfoxide (criss-cross), formamide (open square), and water(open circle) with the bad solvent ethanol as the minor component.The FSPs of dextran are represented by an asterisk. The oval indicatesa range of FSP values where relatively good solvents for dextran canbe found

1308 Colloid Polym Sci (2010) 288:1301–1312

three fractional solubility parameters. The main trend thatwe observe in Fig. 7 is that Rcoil decreases as the fH valuesincrease and as the fD and fP values decrease. Thedependence of Rcoil on any of the three FSPs is ratherweak (correlation factor, R=0.53–0.63). In the case ofbinary mixtures of good solvents for dextran, we identifiedstronger correlations between Rcoil and FSPs, where thedependence of Rcoil on fH emerged to be the morepronounced (R=0.84) [15]. We will next examine thepossible correlation of our dextran solution data to thesolvent surface tension that also expresses cohesive forcesbetween the solvent molecules.

Surface tension

In Fig. 8, we plot the Rcoil values of dextran in water–ethanol and DMSO–ethanol mixtures against their surfacetension values (surface tension data for these two mixtures,but not the other two that we have examined, are available

in [6]). We observe that the dextran coils contracted whenthe good+bad solvent mixtures moved towards smallersurface tensions. This is the opposite from what we hadfound in the case of single or mixed solvents good fordextran where [η] and Rcoil decreased while σ increased[14, 15]. We had interpreted this trend to signify that, whenthe cohesive forces (as captured by the surface tension)between the solvent molecules become stronger, it becomesmore difficult for dextran to break them and to swell withthe solvent. In the present case, cohesive forces asexpressed by the surface tension do not appear sufficientto describe the bad solvent effect on the conformation ofdextran. At this time, it is not clear whether we arecapturing a general bad+good solvent effect or an effectthat is specific to ethanol. Ethanol is known to interactstrongly with the other solvents through hydrogen bonding,and its role in the solvation of dextran may be the result of acomplex interplay of interactions. Further work, includingmolecular modeling, would be needed to clarify this issue.

12

13

14

15

16

17

18

19

20

10 20 30 40 50 60

fD

fP

fH

f

75% Dimethylsulfoxide / 25% Ethanol

Dimethylsulfoxide

12

13

14

15

16

17

18

19

20

10 20 30 40 50 60

fD

fP

fH

f

75% Ethanolamine / 25% Ethanol

Ethanolamine

65% Ethanolamine / 35% Ethanol

12

13

14

15

16

17

18

19

20

10 20 30 40 50 60

fD

fP

fH

Rco

ilR

coil

Rco

ilR

coil

f

30% EtOH

25% EtOH

15% EtOH

100% Water

12

13

14

15

16

17

18

19

20

10 20 30 40 50 60

fD

fP

fH

f

75% Formamide / 25% Ethanol

Formamide

85% Formamide / 15% Ethanol

a

b

c

d

Fig. 6 Coil radius, Rcoil (nm), of dextran T500 plotted vs. the (+)dispersion, fD, (open diamond) polar, fP, and (filled circle) hydrogenbonding, fH, fractional solubility parameters of mixtures of the good

solvent a water, b formamide, c dimethylsulfoxide, or d ethanolaminewith the bad solvent ethanol at 20 °C. The dashed lines indicate the fP,fD, fH values (in order of appearance) of pure ethanol

Colloid Polym Sci (2010) 288:1301–1312 1309

Conclusions

We investigate here the structure and dynamics of thecommon polymer dextran in binary mixtures of a goodsolvent (water, formamide, dimethylsulfoxide, or ethanol-

amine) and a bad solvent (ethanol) using SAXS andviscosity measurements. The experimentally determinedintrinsic viscosity (from which Rcoil is calculated) and Rg

for the dextran T500 fraction (weight average molecularweight=500,000) are discussed in terms of solvent quality.

In all cases, the dextran coil radius decreased with theaddition of the bad solvent (ethanol), reflecting aworsening of the solvent conditions. The change in theRg values upon addition of a fixed (25% v/v) amount ofethanol was approximately 30% for the ethanolamine andformamide cases and less pronounced, 20%, in theaqueous ethanol mixture. Ethanol had a more pronouncedeffect on the dextran DMSO solutions where 6.25%v/vethanol was enough to cause a 5% Rcoil change. Thequality of single solvents for dextran followed the order:ethanolamine > DMSO > formamide > water. Uponaddition of over 20%v/v ethanol, this order changed to:ethanolamine > formamide > DMSO > water.

The relative Rcoil change of dextran in good plus badsolvent mixtures is discussed in terms of the H bondingdensity of the solvent. For the three binary solventmixtures, formamide–ethanol, DMSO–ethanol, and etha-nolamine–ethanol, the same number (approximately 28) ofH bond sites/nm3 is needed to result in a given (5%) Rcoil

change. The H-bonding density can thus be a validindicator of dextran solvation in single or mixed solvents.Water appears as an outlier, with 58 H-bond sites/nm3 in thewater–ethanol mixed solvent needed for a 5% Rcoil

decrease.Upon heating, the polymer segments adopt a less

expanded conformation in the solution. This can beattributed to a decreased H bonding stability of the solventmolecules at higher temperature, resulting in an enhance-ment of the intermolecular association between polymer

12

13

14

15

16

17

18

19

20

10 20 30 40 50 60

y = 7.0066 + 0.32848x R= 0.63604

Rco

ilR

coil

Rco

il

30% Ethanol

25% Ethanol

15% Ethanol

75% Formamide / 25% EtOHWater

Formamide

Ethanolamine

75% Ethanolamine / 25% EtOH

85% Formamide / 15% EtOH

65% Ethanolamine / 35% EtOH75% Dimethylsulfoxide / 25% EtOH

DMSO

12

13

14

15

16

17

18

19

20

10 20 30 40 50 60

y = 12.079 + 0.13286x R= 0.52225

fP

fD

fH

30% Ethanol

25% Ethanol

15% Ethanol

75% Formamide / 25% EtOHWater

Formamide

Ethanolamine

75% Ethanolamine / 25% EtOH

85% Formamide / 15% EtOH

65% Ethanolamine / 35% EtOH

DMSO

75% Dimethylsulfoxide / 25% EtOH

12

13

14

15

16

17

18

19

20

10 20 30 40 50 60

y = 19.659 - 0.090209x R= 0.55268

30% Ethanol

25% Ethanol

15% Ethanol

75% Formamide/25% EtOHWater

Formamide

Ethanolamine

75% ethanolamine/25% EtOH

85% Formamide/15% EtOH

65% ethanolamine/35% EtOH

DMSO

75% Dimethylsulfoxide / 25% EtOH

a

b

c

Fig. 7 Coil radius, Rcoil (nm), of dextran T500 plotted vs. adispersion, fD, b polarity, fP, and c hydrogen bonding, fH, fractionalsolubility parameters of single and mixed solvents at 20 °C. Thedotted lines are linear fits to all the data in each plot

12

13

14

15

16

17

18

19

20

30 40 50 60 70 80

Rco

il (n

m)

σ (μΝ /m)

100% DMSO

100% Water

75% DMSO

70% Water

75% Water

85% Water

Fig. 8 Coil radius, Rcoil, of dextran T500 plotted vs. the surfacetension, σ, of the single and mixed solvents at 20 °C (the volumepercent content of the main solvent component is indicated in thegraph; the remainder is ethanol)

1310 Colloid Polym Sci (2010) 288:1301–1312

segments. The temperature effect that we observe is not assignificant as the effect of bad solvent addition on the coilconformation of dextran.

We examined whether the solvent effects on the dextrancoil radius can be rationalized in terms of changes inproperties of the solvent mixtures such as fractionalsolubility parameters and the surface tension. A commonobservation is that Rcoil decreased as the solvent FSPsmoved towards the FSP values of ethanol. However, theRcoil data did not show a strong correlation when plotted vs.FSPs. There is an indication that an increase of the solventH bonding FSP relative to the polar FSP contribution leadsto a decrease in the dextran Rcoil. When plotted against thesolvent surface tension, the dextran coil dimensionsdecrease as σ decreased. This finding appears counterintu-itive, as decreasing surface tension means decreasingsolvent cohesive forces which would otherwise be expectedto facilitate swelling of the polymer coil with solvent, butmay reflect specific interactions involving ethanol.

Acknowledgements We thank NSF (grants CBET 0124848/TSEand 0421154/MRI) for supporting this research.

References

1. Mizoguchi K (1995) Opto-electronic polymers for advancedcomputer and communication technologies. Polym Adv Technol6:15–24

2. Pennadam SS, Firman K, Alexander C, Górecki DC (2004)Protein–polymer nano-machines. Towards synthetic control ofbiological processes. J Nanobiotechnology 2(8):1–7

3. Waigh TA (2007) Applied biophysics: a molecular approach forphysical scientists. Wiley: Chichester, UK

4. Hamley IW (2000) Introduction to soft matter. Wiley5. Sperling LH (2001) Introduction to physical Ppolymer science,

3rd edn. Wiley-Interscience. New York, NY6. Marcus Y (2002) Solvent mixtures: properties and selective

solvation. Dekker. New York, NY7. Hammouda B, Worcester D (2006) The denaturation of DNA in

mixed solvents. Biophys J 91:2237–22428. Alexandridis P, Andersson K (1997) Reverse micelle formation

and water solubilization by polyoxyalkylene block copolymers inorganic solvent. J Phys Chem B 101:8103–8111

9. Holmqvist P, Alexandridis P, Lindman B (1997) Phase behaviorand structure of ternary amphiphilic block copolymer–alkanol–water systems: comparison of poly(ethylene oxide)–poly(propyl-ene oxide) to poly(ethylene oxide)–poly(tetrahydrofuran) copoly-mers. Langmuir 13:2471–2479

10. Schmidt G, Richtering W, Lindner P, Alexandridis P (1998) Shearorientation of a hexagonal lyotropic triblock copolymer phase asprobed by flow birefringence and small-angle light and neutronscattering. Macromolecules 31:2293–2298

11. Yang L, Alexandridis P (2000) Polyoxyalkylene block copolymersin formamide–water mixed solvents: micelle formation andstructure studied by small-angle neutron scattering. Langmuir16:4819–4829

12. Ivanova R, Lindman B, Alexandridis P (2002) Effect ofpharmaceutically acceptable glycols on the stability of the liquid

crystalline gels formed by Poloxamer 407 in water. J ColloidInterface Sci 252:226–235

13. Sakai T, Alexandridis P (2005) Spontaneous formation of goldnanoparticles in poly(ethylene oxide)–poly(propylene oxide)solutions: solvent quality and polymer structure effects. Langmuir21:8019–8025

14. Antoniou E, Buitrago CF, Tsianou M, Alexandridis P (2010)Solvent effects on polysaccharide conformation. CarbohydrPolym 79:380–390

15. Antoniou E, Alexandridis P (2010) Polymer conformation inmixed aqueous polar organic solvents. Eur Polym J 46:324–335

16. Dickinson E, Walstra P (1993) Food colloids and polymers:stability and mechanical properties. The Royal Society ofChemistry. Cambridge, UK

17. Glass E (1989) Polymers in aqueous media: performance throughassociation. ACS. Washington, DC

18. De Belder AN (2002) Dextran. Ullmann's encyclopedia ofindustrial chemistry. Wiley-VCH. New York, NY

19. Armstrong JK, Wendy RB, Meiselman HJ, Fisher TC (2004) Thehydrodynamic radii of macromolecules and their effect on redblood cell aggregation. Biophys J 87:4259–4270

20. Gekko K (1981) Solution properties of dextran and its ionicderivatives. ACS Symp Ser 150:415–438

21. Güner A (1999) Unperturbed dimensions and theta temperature ofdextran in aqueous solutions. J Appl Polym Sci 72:871–876

22. Da Silva DC, Ricken I, Silva MA, Machado VG (2002) Solute–solvent and solvent–solvent interactions in the preferentialsolvation of Brooker’s merocyanine in binary solvent mixtures. JPhys Org Chem 15:420–427

23. Nain AK (2007) Densities and volumetric properties of (formam-ide+ethanol, or 1-propanol, or 1,2-ethanediol, or 1,2-propanediol)mixtures at temperatures between 293.15 K and 318.15 K. J ChemThermodyn 39:462–473

24. Güner A (2004) The algorithmic calculations of solubilityparameter for the determination of interactions in dextran/certainpolar solvent systems. Eur Polym J 40:1587–1594

25. Hiemenz PC, Rajagopalan R (1997) Principles of colloid andsurface chemistry, 3rd edn. Marcel Dekker. New York, NY

26. Tirtaatmadja V, Dunstan DE, Boger DV (2001) Rheology ofdextran solutions. J Non-Newton Fluid Mech 97:295–301

27. Antoniou E, Tsianou M (2010) Solution properties of dextran inwater and in formamide. J Appl Polym Sci (in press)

28. Flory PJ (1953) Principles of polymer chemistry. CornellUniversity Press: Ithaca, NY

29. Anderson TW (1984) An introduction to multivariate statisticalanalysis, 2nd edn. Wiley

30. De Gennes P-G (1993) Scaling concepts in polymer physics.Cornell University Press: Ithaca, NY

31. Evans DF, Wennerström H (1999) The colloidal domain: wherephysics, chemistry, biology, and technology meet, 2nd edn. Wiley-VCH

32. Joseph R, Devi S, Rakshit AK (1991) Viscosity behavior ofacrylonitrile–acrylate copolymer solutions in dimethyl formamide.Polym Int 26:89–92

33. Horkay F, Hammouda B (2008) Small-angle neutron scatteringfrom typical synthetic and biopolymer solutions. Colloid PolymSci 286:611–620

34. Çatiker E, Güner A (1998) Unperturbed molecular dimensionsand the theta temperature of dextran in dimethysulfoxide (DMSO)solutions. Polym Bull 41:223–230

35. Lirova BI, Smolyanskii AL, Tager AA (1971) Infrared absorptionstudy of the molecular interactions in solutions of polyvinylalcohol and its low-molecular analogs. J Applied Spectrosc,Translated from Zhurnal Prikladnoi Spektroskopii 15:491–497

36. Sato T, Chiba A, Nozaki R (1999) Dynamical aspects ofmixing schemes in ethanol–water mixtures in terms of the

Colloid Polym Sci (2010) 288:1301–1312 1311

excess partial molar activation free energy, enthalpy, andentropy of the dielectric relaxation process. J Chem Phys110:2508–2521

37. Bellissent-Funel M-C, Nasr S, Bosio L (1997) X-ray and neutronscattering studies of the temperature and pressure dependence ofthe structure of liquid formamide. J Chem Phys 106:7913–7919

38. Hakem IF, Boussaid A, Benchouk-Taleb H, Bockstaller MR(2007) Temperature, pressure, and isotope effects on the structureand properties of liquid water: a lattice approach. J Chem Phys127:224106

39. Hansen CM (2000) Hansen solubility parameters “a usershandbook”. CRC Press: Boca Raton, FL

1312 Colloid Polym Sci (2010) 288:1301–1312