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Investigation of critical concentrationsof poly(vinyl pyrrolidone) in N, N-dimethylformamide by a viscositytechniqueEmna Cherifab, Ons Zoghlamia & Tahar Othmana

a Faculté des Sciences de Tunis, LR99ES16 Physique de la MatièreMolle et Modélisation Electromagnétique, Université de Tunis ElManar, 2092, Tunis, Tunisieb Institut Préparatoire aux Etudes d’Ingénieurs de Tunis,Université de Tunis, 1089, Monfleury, TunisPublished online: 17 Jul 2014.

To cite this article: Emna Cherif, Ons Zoghlami & Tahar Othman (2014): Investigation of criticalconcentrations of poly(vinyl pyrrolidone) in N, N-dimethylformamide by a viscosity technique,Physics and Chemistry of Liquids: An International Journal, DOI: 10.1080/00319104.2014.937864

To link to this article: http://dx.doi.org/10.1080/00319104.2014.937864

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Investigation of critical concentrations of poly(vinyl pyrrolidone) inN, N-dimethylformamide by a viscosity technique

Emna Cherif a,b*, Ons Zoghlamia and Tahar Othmana

aFaculté des Sciences de Tunis, LR99ES16 Physique de la Matière Molle et ModélisationElectromagnétique, Université de Tunis El Manar, 2092, Tunis, Tunisie; bInstitut Préparatoire aux

Etudes d’Ingénieurs de Tunis, Université de Tunis, 1089, Monfleury, Tunis

(Received 15 April 2014; final version received 2 June 2014)

The viscosity of solutions of poly(vinyl pyrrolidone) (PVP) in N,N-dimethylforma-mide over a wide range of concentrations and at different temperatures was measured.The polymer solutions exhibited a critical concentration c**, separating dilute solu-tions into extremely dilute solutions and dilute solutions. The viscosity–temperaturedependence is discussed on the basis of a formula of the correlation between the trueand the experimental relative viscosity. The results revealed that an abnormal viscosityof neutral PVP solutions in the dilute solution region (c › c**) and extremely dilutesolutions (c ‹ c**) can be ascribed to interface effects. The polymeric solutes werereadily adsorbed on the wall surface of the cone-plate rheometer, which greatlyinfluenced the viscosity measurements of the PVP solutions and resulted in theapparent abnormal viscosity behaviour. The intrinsic viscosity [η] and the Hugginsconstant kH, were calculated. The solute adsorption behaviours and structural informa-tion of the polymer were discussed in depth.

Keywords: viscosity–temperature; polymer solution; poly(vinylpyrrolidone); intrinsicviscosity

1. Introduction

On the basis of dynamic measurements (cone-plate rheometer) and using a mixture ofpolymers dissolved in a common solvent, a critical concentration c** that separates regiondilute solutions into extremely dilute solution (c ‹ c**) and dilute solution (c › c**) wasestablished [1–3]. This critical concentration has also been established by using only onepolymer dissolved in a pure solvent [4,5]. For one polymer, c** increases with thedecrease of the hydrodynamic volume of the macromolecular chains or with the increaseof their segment density. Expressing the segment density of the chains by the inverse ofintrinsic viscosity [η], linear relationships between this quantity and c** (c** = 2.5 10−2

[η]−1) were obtained [4].Linear relationships have also been obtained between the inverse of the intrinsic

viscosity and the overlapping concentration c* [6,7], introduced by de Gennes, whichseparates the dilute solutions from the semi-dilute solutions.

It was proposed [3] that at the critical concentration c** the macromolecular chainsundergo an incipient overlapping that results in a decrease of their hydrodynamic volume.Nevertheless, the macromolecular chains conserve their individuality even above c**, andlose their individuality only at the overlapping concentration c*. An individual chain

*Corresponding author. Email: amna_cherif@yahoo.fr

Physics and Chemistry of Liquids, 2014http://dx.doi.org/10.1080/00319104.2014.937864

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occupies a certain domain in the solution, inside of which the segment density decreasesfrom the central to the peripheral region.

Despite a considerable number of theoretical and experimental studies [8–10], thecurrent understanding of the anomalous viscosity behaviour of neutral polymer solutionsat low concentrations is still far from complete. In dilute polymer solution, the relativeviscosity (ηr) is proportional to concentration c, as indicated by the Huggins equation(ηr = 1 + [η]c + kH[η]

2c2). In extremely dilute polymer solutions, however, the linearrelationship between (ηr) and c has never been obtained experimentally. In particular, theviscosity behaviour of neutral polymer solutions at low concentrations is still somewhat asubject of controversy, due to the fact that completely different experimental results havebeen presented and interpreted.

Interestingly, from viscosity measurements of neutral polymer solutions it was alsofound that the reduced viscosity ηred (ηred = (ηr −1)/c) deviated from the Huggins equationand there was not a linear dependence between reduced viscosity and concentration in thelow concentration region. The viscosity curve appeared to be upward or downwardbending [11,12]. Cheng et al. [13,14] systematically studied the abnormal viscositybehaviours of neutral polymers in extremely dilute solutions and confirmed that thosephenomena could be ascribed to an interfacial effect. The upward bending was caused byadsorption to the cone and plate surfaces which occurred in the cone-plate rheometer inthe process of viscosity measurements, while the downward bending was due to atransition from viscous to slip flow.

Cheng et al. corrected the apparent relative viscosity ηr data obtained from theEinstein viscosity equation on the basis of the interface effect on polymers viscositymeasurement of dilute solutions with the Langmuir adsorption model. Their quantitativeexpression to describe the experimental relative viscosity (ηr,exp) and true relative viscos-ity (ηr, theo) is shown below [15]:

ηr;exp ¼ ηr;theo 1þ kc= cþ cað Þð Þ (1)

(1 + kc /(c + ca)) is the interfacial interaction contribution to the relative viscosity ofpolymer solutions , ca is the particular concentration at which half the active sites of theviscometer wall have adsorbed polymers and k denotes the maximum fractional change offlow time of pure solvent due to the variation of the surface properties of the viscometerwall in the course of determining the polymer solution viscosity. It is worthy to note thatthe constant k may be either positive or negative depending on whether the flow time ofthe solvent is increased or decreased after the adsorption of the polymer. If the flow timeof the solvent increases after adsorption of the polymer, k > 0 and the curvature isupwards. The opposite phenomenon may also occur. In other words, it is possible thatthe flow time of the solvent will decrease after adsorption of the polymer. In this case,k < 0, the curvature is downward. The increase of the slip flow time of the solventdepends on the nature of the absorbed polymer and the interaction between the absorbedpolymer and the solvent.

2. Viscosity of extremely dilute solutions

Theoretically, in the extremely dilute concentration region, both hydrodynamic andthermodynamic polymer–polymer intermolecular interactions are absent. In this case,

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the Einstein viscosity law is applicable. In this concentration region, the relative viscosityvaries linearly with concentration and may be expressed as

ηr;theo ¼ 1þ η½ �c (2)

Therefore, inserting Equation (2) into Equation (1), we have the expression of theconventionally reduced viscosity ηred as

ηr;exp ¼ 1þ η½ �cð Þ 1þ kc= cþ cað Þð Þ (3)

ηred ¼ ηr;exp � 1� �

=c ¼ η½ � 1þ kc= cþ cað Þð Þ þ k= cþ cað Þ (4)

where [η] is intrinsic viscosity or limiting viscosity number in the extremely diluteconcentration region, ca is the particular concentration at which half the active sites ofthe viscometer wall have adsorbed polymers and k is a parameter related to the adsorptionlayer thickness.

At the extremely dilute concentration region, from Equation (4) we have the extra-polated value of the reduced viscosity to infinitive dilution

limc!0

ηred ¼ η½ � þ k=ca (5)

3. Viscosity in dilute solution region

For the purpose of determining the intrinsic viscosity of polymer solutions, measurementsare usually carried out in the concentration region with relative viscosities from 0.12 to0.25. In this dilute solution region, intermolecular interactions are operative and therebythe theoretical relative viscosity should include a higher order term such as

ηr;theo ¼ 1þ η½ �c þ kH η½ �2c2 (6)

in which kH is the Huggins slope constant. Inserting Equation (6) into Equation (1), wehave the reduced viscosities ηred of dilute polymer solutions

ηr;exp ¼ 1þ η½ �c þ kH η½ �2c2� �

1þ kc= cþ cað Þð Þ (7)

ηred ¼ k= cþ cað Þ þ η½ � 1þ kc= cþ cað Þð Þ þ kH η½ �2c= 1þ kc= cþ cað Þð Þ (8)

4. Experimental

The poly(N-vinyl-pyrrolidone) (PVP) was a commercial product of Sigma-Aldrich Co.(Germany). The weight-average molecular weight was 24.000 g/mol. N,N-dimethylfor-mamide (DMF) was purchased from Merck Chemical Co. (Germany), and had a reportedmass fraction purity of 0.995.

The apparatus used was a cone and plate type viscometer Brook Field DV-II (+Pro Co;Germany). This device is equipped with a motor which produces a deformation of the

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sample and a sensor which measures the strain induced in the sample as a function ofshear rate. The temperature was controlled to a ± 0.5° using a thermostated water bath,Haake type D8 (Germany). The system was controlled by a computer.

5. Results and discussion

5.1. Effet of adsorption on the viscosity of the dilute polymer solutions

Figure 1 shows the variation of ηred of mixture of PVP in DMF with the concentration ofPVP at the four investigated temperatures of 25°C, 30°C, 35°C and 40°C. Figure 1deserves some comments:

● The polymer PVP has polyelectrolyte behaviour in DMF; the reduced viscosityvalue decreased with increasing concentration of polymer solution due to thecontribution of intermolecular interactions of the polymer chains, which is causedby the intra-molecular hydrophobic association between hydrophobic groups on thePVP.

● The decrease of the reduced viscosity of PVP in DMF can be attributed to therepulsive intermolecular interactions between PVP–PVP and PVP in solution.

0.16

0.18

0.20

0.22

0.24

0.26

0.28

0.30

c** = 0.412 g/dl

c** = 0.453 g/dl

c** = 0.472 g/dl

c** = 0.431 g/dl

T = 25 ºC

T = 35 ºC T = 40 ºC

T = 30 ºC

η re

d d

l /g

η re

d d

l /g

η re

d d

l /g

η re

d d

l /g

c (g/dl)

a)

0.15

0.20

0.25

0.30

0.35

c (g/dl)

b)

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

c (g/dl)

c)

0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 1.0

0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 1.0

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.55

c (g/dl)

d)

Figure 1. Variation of reduced viscosity of PVP in DMF with concentration of PVP at (a)T = 25oC, (b) T = 30oC, (c) T = 35oC and (d) T = 40°C. c** is the critical concentration.

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Tewari and Srivastava [16] pointed out that the most important polymer–polymerinteraction is the thermodynamic interaction that includes the intramolecularexcluded volume effect, resulting in an expansion of the coil in solution, and theintermolecular excluded volume effect, resulting in a contraction of the coil. Therepulsive intermolecular interaction between PVP–PVP and PVP in solution willincrease the intermolecular excluded volume effect.

● As we can see in this figure, the crossover point, which indicates the criticalconcentration c**, that separates the dilute solutions in to extremely dilute solutions(c ‹ c**) and dilute solutions (c › c**), moved to higher concentrations withincreasing temperature. The lowering of ηred must be attributed to a compressionof the chains due to repulsive interactions between them. The experimentallydetermined values of c** are summarised in Table 1.

● The curves show a rather sharp upward turning appears in the extremely diluteconcentration region. The reduction of the reduced viscosity modifies the (1 + kc/(c + ca)) and causes the value of the reduced viscosity increases with concentrationto decrease, and exhibit little change at different temperatures.

5.2. The temperature dependence of the parameters of Equation (8)

The results of the effect of temperature on the intrinsic viscosity of PVP are shown inFigure 2(a); the intrinsic viscosity increased from 0.4 dl/g to 0.8 dl/g by increasing thetemperature from 25°C to 40°C. These results indicate that the effect of temperature onthe intrinsic viscosity of PVP is significant. Thermodynamically, low temperatures arefavoured for polymer–solvent interactions. It is well known that [η] reflects the hydro-dynamic volume of a polymer single chain in an extremely dilute solution [4]. With theincrease of temperature, the PVP intra-chain hydrogen bonds become dominant, and thestiffness of the PVP chains increased, which makes the local chain quite stiff and have alarge hydrodynamic volume and intrinsic viscosity. The considerable increase in theintrinsic viscosity of PVP with increasing temperature in DMF is due to the stronghydrogen-bond-type interaction between PVP and DMF. This attractive interaction coun-teracts the intermolecular-excluded volume effect. Therefore, the intrinsic viscosity ofPVP in the polymer–solvent PVP + DMF increased with increasing temperature becausethe PVP coils were expanded due to the intramolecular excluded volume effect.

The parameters ca and k are physically mutually related; both of them reflect thecapacity of adsorption and depend on the coverage and contacting surface of the visc-ometer with the polymer solution. Hence, the dimensions of the cone-plate rheometer,measuring and reservoir bulb, volume of solution used, the saturation amount of adsorp-tion, etc., all have an influence on the magnitude of these two parameters. In addition,they are regarded as adjustable parameters in the data fitting process.

Table 1. Least-squares fitted values of the parameters of Equation (4) for PVP + DMF systems asfunctions of the temperatures. Values for the parameters of Equation (8) are given in parentheses.

T (°C) [η] (dl/g) k ca (g/dl) kH c**(g/dl) Beff/R

25 0.370 (0.365) 0.676 (0.668) 0.122 (0.084) (1.386) 0.412 0.12130 0.567 (0.552) 0.758 (0.857) 0.037 (0.096) (0.733) 0.431 0.13135 0.706 (0.821) 0.841 (0.854) 0.052 (0.105) (0.443) 0.453 0.14240 0.820 (0.948) 0.926 (0.954) 0.191 (0.114) (0.342) 0.472 0.151

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Figure 2(b) presents the temperature dependence of the parameter k.The curve in Figure 2(c) shows the influence of temperature on the parameter kH that

is the best fit in Equation (8) of the reduced viscosity versus the temperature. kH decreasedas the temperature increased. The Huggins constant is a hydrodynamic parameter thatdepends on the size and shape of the species in solution. The Huggins constant will betemperature-dependent only in polymers easily associating in solution, either by the effectof strong ionic or polar interactions or by the effect of hydrogen bonds. For the PVP inDMF, hydrogen bonds were formed between the OH groups in PVP and nitrogen atoms inpyridine groups of DMF.

Figure 3 presents the critical concentration c** and the particular concentration ca ofPVP in DMF solution at varied temperatures. Both c** and ca increased with temperatureincrease.

5.3. The intrinsic viscosity dependence of the parameters (c** , kH and beff/R )

The intrinsic viscosity dependence of c** is shown in Figure 4(a). It is noted that the c**increases nonlinearly with [η] as determined by

c�� ¼ 0:402� 0:022 η½ � þ 0:132 η½ �2 (9)

24 27 30 33 36 39

0.4

0.6

0.8

(a)

0.64

0.72

0.80

0.88

0.96(b)

k

0.3

0.6

0.9

1.2

1.5

(c)k

H

T ( ºC)

[η]

(dl /g

)

Figure 2. Effect of temperature on the intrinsic viscosity [η] (a), the parameter k (b) and theHuggins constant kH (c) of PVP + DMF.

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24 26 28 30 32 34 36 38 40 42

0.09

0.10

0.11

(a)

0.42

0.44

0.46

0.48

(b)

T ( ºC)

ca (

g / d

l)c

** (

g / d

l)

Figure 3. Temperature dependence of the critical concentration c** (b) the particular concentrationca (a) of PVP + DMF.

0.4 0.5 0.6 0.7 0.8

0.42

0.45

0.48

(a)

0.5

1.0

1.5(b)

0.12

0.13

0.14

0.15

(c)

kH

c**

(g

/ d

l)b

eff / R

[η] (dl /g)

Figure 4. Intrinsic viscosity dependence of the parameters: (a) the critical concentration (c**),(b) the constant of Huggins kH and (c) beff/R.

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The relationship between kH and [η] is presented in Figure 4(b). kH decreasesnonlinearly with [η]. The scaling laws obtained between [η] and kH was as follows:

kH ¼ 0:26 η½ ��1:6 (10)

k in Equation (1) is a parameter related to the adsorption layer thickness. Furthermore, theeffective thickness of the adsorbed layer beff [14] could be evaluated from the parameter kcoupled with the radius (R) of the cone-plate rheometer .

beff=R ¼ 1� 1þ kð Þ�1=4 (11)

According to Equation (11), the ratio of the effective adsorption thickness beff to theradius (R) of the cone-plate rheometer was calculated and listed in Table 2 also. Figure 4(c) presents the calculated beff/R as a function of intrinsic viscosity [η], beff/R has asignificant effect on [η]. [η] increases as beff/R increases. Hence, one can confirm that thestiffness of polymer chains increases, resulting in the increase of intrinsic viscosity andthis effective thickness. c**, kH and beff/R of the present systems varied nonlinearly withthe intrinsic viscosity, and the three properties have been explained by using the followingequation [17]:

Y ¼ AYexp½�BY=ð η½ � � η½ �0YÞ� (12)

Y refers either to the c**, kH or beff/R . The least-squares fitted values of AY, BY and [η]0Yare presented in Table 2.

This non-linear result is expected between the PVP and the DMF. The parameter BY

can be interpreted as being based on three factors, namely physical, chemical andstructural effects. The physical effects involve dispersion forces and non-specific interac-tions in the solution. The chemical and specific interactions result in the increase of theconcentration of DMF. Therefore, these chemical effects contribute negative values toBc** and Bbeff/R. The structural effects that arise from the geometrical fitting of onecomponent into the other are due to the different molar volumes and free volumes ofpure components and positive contributions to AY.

6. Conclusions

In summary, based on a systematic study of the viscosity behaviours of solutions of PVPin N,N-dimethylformamide (DMF), the polymer could be ascribed to interface effect inviscous flow. The viscosity behaviours of dilute polymer were described, which reflectedthe structural state of polymer in solution and at the cone-plate rheometer wall. According

Table 2. Least-squares fitted values of the parameters ofEquation (12) for PVP and DMF.

Y AY BY (dl/g ) [η]0Y (dl/g )

c** 0.078 (g/dl) −9.655 6.214kH 0.006 7.149 −0.957beff/R 0.018 −7.767 4.534

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to this theory, the structure of polymers in solution and at the interface of the cone-platerheometer could be explored by studying their viscosity behaviours in dilute solutions.

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