http://www.e-polymers.org e-Polymers 2007, no. 020 ISSN 1618-7229

Investigation of Poly(vinyl pyrrolidone) in methanol by dynamic light scattering and viscosity techniques

Adel Aschi*, Mohamed Mondher Jebari and Abdelhafidh Gharbi

Laboratoire de Physique de la Matière Molle, Faculté des Sciences de Tunis, Campus Universitaire, 1060, Tunisia; Fax +216.71.885.073; email : [email protected] yahoo.fr

(Received: 17 November, 2006; published: 16 February, 2007)

Abstract: The behavior of poly(vinyl pyrrolidone) (PVP) in methanol was examined using several independent methods. The hydrodynamic radius (Rh) of individual samples, over a range of molecular weights (10,000–360,000), was determined using dynamic light scattering (DLS) measurements. Dynamic Light Scattering (DLS) techniques directly probe such dynamics by monitoring and analyzing the pattern of fluctuations of the light scattered from polymer molecules. Some viscosity measurements were also performed to complete the DLS measurements and to provide more information on the particle structure. The results obtained with PVP–methanol system showed that plotting the variation of intrinsic viscosity versus the logarithm of the molecular mass of this polymer, we observe one crossover point. This crossover point appears when we reach the Θ-solvent behavior and delimit two molecular mass regions. The second order least-squares regression was used as an approach and was in excellent agreement with viscometric experimental results. Keywords: DLS, Hydrodynamic radius, intrinsic viscosity.

Introduction Polymers are frequently employed in many industrial and pharmaceutical applications. As a result, this has prompted a large volume of fundamental studies to understand the kinetic equilibrium, structural, and rheological properties of many different systems. Poly(vinyl pyrrolidone) (PVP, Sigma Chem, Mw = 10 000, 24 000, 40 000 and 360 000) has been used in a large number of different applications. The best known is its use in the pharmaceutical, in the cosmetic industry (e.g. tablet binders and hair fixative preparations respectively) and in the construction industry (in plywood adhesives and sealing composites). Recently, the polymer has also been utilized in electrotechnics, electro-optics and in the production of selective membranes [1– 4]. PVP often achieves the desired success because it exhibits a unique combination of properties. This range of properties can be extended almost without limit when the copolymers made from Vinyl pyrrolidone are taken into consideration with other monomers. Finally, PVP is a white and hygroscopic powder. In contrast with most polymers, it is readily soluble both in methanol and in a large number of organic solvents, such as alcohols, amines, acids, amides and lactams. In diluted solutions, the interactions between polymer chains are negligible, and the behavior of the sample is dictated by the balance among intra-molecular polymer– polymer and intermolecular polymer–solute interactions, which depend on the quality of the solvent. Thus, in good solvents, the polymer–solvent is more favorable; the

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polymeric chain tends to solvate, minimizes the number of polymer–polymer contacts and produces a rather large excluded volume. On the contrary, in poor solvents, the polymer–polymer interactions are preferred; the polymer units try to avoid contact with the solvent, and the number of polymer–polymer contacts increases, producing a collapse of the chain that gives rise to a negative value of the excluded volume. The hydrodynamic radius Rh is a very convenient magnitude to express the molecular dimensions of a polymer chain because, in the first place, it can be directly obtained from dynamic light scattering data, and its definition is applicable to macromolecules of any shape [5-7]. Furthermore, the value of Rh for a given body, a polymer chain, is related to its mass by simple mathematical relationships, called scaling laws, whose numerical parameters depend on the shape of the body. Thus, the analysis of experimental values of Rh as a function of molecular weight affords information on the shape of the polymer chain. Recently, Tarazona and coauthors have shown, that log–log plot of the radius of gyration versus molecular weight for PVP in water containing a 0.1 M concentration of NaNO3, shows a slight curvature at low molecular weights and the slope of the linear part yields ν = 0.4 [8]. Previous reports have shown that the intrinsic viscosity of PVP at finite concentration, decreases with an increase in the concentration of PVP in solution [9] and also shown that the effect of temperature on viscosity behavior of PVP in methanol shows that the interaction parameter increases up to maximum value, and decreases after a certain temperature [9]. The same behavior was shown for a solution of the PVP in water and that was explained by the change of the conformation which had occured as a result of the rotational freedom around -C-C- single bonds within the PVP molecule in moderately dilute solution [10, 11]. Further more, vinyl polymers contain methylene units in their main chain as the spacer, which would relieve steric repulsion between the side chain substituents and the chain becomes a less-flexible polymer [12]. In this work, we report some dynamic light scattering and viscosity results to explain the behavior of the Poly-(vinyl-pyrrolidone) (PVP) in methanol and in diluted regime. In our case, two domains of molecular mass are well delimited, because for this polymer we observe a well-determined crossover point in the variation of their solution dimensions as a function of their molecular mass. More precisely, in the Mark Houwink-Sakurada (MHS) representation we observe a well defined crossover point in which we have a variation of the exponent of these equations. Thus we distinguish two regions of molecular mass: region I, below the crossover point; region II above the crossover point. This phenomenon was not noticed in the case of the variation of hydrodynamic radius as a function of the molecular masses. In this article we also propose an equation, based on the second order least-squares regression, relating the intrinsic viscosity to the molecular mass of polymer as a special case to determine, in the other hand, the approximate values of Mark- Houwink-Sakurada exponents [13]. Still, the motivation of this study came from the observation of difference between the molecular weight Mw and “viscosity-average” molecular weight Mη, especially at higher masses [14]. Some experimental analyses explain this effect by the affectation of Mark-Houwink-Sakurada relationship by the polydispersity [15, 16]. However, such phenomenon may be still explained by the rigidity of polymer chains [17-21].

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Results and discussions

Fig. 1 shows plot for the four PVP molecular weights Mw, in methanol at 25°C. The figure shows, in a diluted regime, the diffusion coefficient increases with the concentration and with a positive slope. As seen, the data points for each system follow a straight line, and therefore D0 and kD may be determined from the ordinate intercept and slope, respectively. The slopes indicate a positive second virial coefficient and a situation of good solvent conditions (A2 increases), 2A2M > ks + w. In Table 1 are given the values of D0 and kD.

200

150 /s] 2 cm 8 - 100 [10 D

50

0 012345678 C [mg/ml]

Fig. 1. Dynamic light scattering measurements of the diffusion coefficient D as a function of polymer concentration for different molecular weight. (▲) Mw = 10 000, (■) -1 Mw = 24 000 g mol , (♦) Mw = 40 000 and (●) Mw = 360 000. The dashed lines are a fit to the Eq. (7).

Tab. 1. Results of DLS Measurements on Poly(vinyl-pyrrolidone) in methanol at T = 25 °C.

-3 -8 2 3 Mw × 10 D0 (10 cm /s) KD (cm /mg) Rh(nm) 10 91.2 0.11 4.6 24 48.9 0.21 8.6 40 40.3 0.26 10.5 360 11.2 1.48 37.4

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We noticed that the absolute diffusion coefficient D0 decreases when the molecular weight increases. Still, the interactions increase as a function of the molecular mass of the chain and their character becomes more and more repulsive.

Another point of interest is the scaling of the hydrodynamic radius (Rh) of the single chain with the molecular weight. Rh can be calculated from the diffusion coefficient in the limit of zero polymer concentration (D0) Tk lim DD == B (1) →0c 0 6πη 0 R h where kBT is the thermal energy and η0 is the solvent viscosity.

In Table 1, the calculated values of hydrodynamic radius Rh are listed. Fig. 2 shows example of Rh measured for different molecular weight fractions. In the panel of the figure, the plot is on a solid line, in agreement with the predicted power relationship; -ν Rh ∝ N . The exponent ν obtained in the fitting is 0.57, slightly smaller than the value predicted for complete excluded volume behavior. Still, the value of the exponent of Flory shows that the methanol might be considered like a good solvent for the PVP. The same behavior was shown for PVP in pure water [22].

102

101 [nm] h R

100 104 105 106

Mw

Fig. 2. log-log plot of the hydrodynamic radius Rh as a function of molecular weight for PVP.

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Intrinsic viscosity For all concentrations, Fig. 3 shows an anomalous behavior (rapid viscosity upswing). The experimental values of [η] for different temperatures and molecular masses are determined by the Eq. (8). There is clear decrease in intrinsic viscosity, [η] with an increase in temperature up to at least 40 °C (Table 2 and Fig. 3).

Tab. 2. Values of intrinsic viscosity of Poly(vinyl-pyrrolidone) in methanol at different temperature.

T °C [η](dL/g) [η](dL/g) [η](dL/g) [η](dL/g) Mw = 10 000 Mw = 24 000 Mw = 40 000 Mw = 360 000 10 0.244 0.501 0.628 1.688 15 0.220 0.480 0.604 1.600 20 0.214 0.472 0.581 1.576 25 0.205 0.467 0.539 1.551 30 0.196 0.459 0.503 1.511 35 0.174 0.443 0.477 1.450 40 0.160 0.434 0.453 1.394

3.5 T10 C T15 C T20 C 3 T25 C T30 C T35 C T40 C

2.5 [dL/g] C / 2 s p η

1.5

1 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 C [g/dL]

Fig. 3. Reduced viscosity ηsp /C of Poly(vinyl pyrrolidone), Mw = 360 000 in methanol, as function of polymer concentration and temperature. The dashed lines correspond to the fit with the equation 8.

This would be indicative of molecular break-down and/or conformational change to a more compact shape, as observed by O. Melad in the case of PVP in DMF [23] and

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by M. Singh et. al in the case of PVP in water [10, 11]. This behavior could be attributed to the smaller structural changes of PVP in methanol, and to the rotational freedom around –C – C- single bonds within monomer units in dilute solution, which results in conformational changes [10, 11]. In fact the most important polymer– polymer interaction is the thermodynamic interaction which includes the intra- molecular excluded volume effect, resulting in an expansion of the coil in solution and the intermolecular excluded volume effect, resulting in contraction of the coil [23, 24].

In order to show the Mw dependence of [η], we have plotted in Fig. 4, log([η]) against a log(Mw), as suggested by the empirical Mark-Houwink relationship, [η] = k Mw , where K and a are two parameters which depend on the solvent and the polymer under study. We noticed a nonlinear variation in log-log form, which suggests that a is not constant but changes with molecular mass. In the Mark–Houwink–Sakurada (MHS) representation, we distinguish two regions of molecular mass. In the molecular mass region below this point or in region I, we have a good linearity between log[η] and log M, as in the case of flexible polymers. The exponent of the MHS equation, for all the temperatures, is slightly lower than 0.8, which corresponds to the appearance of excluded volume behavior. In the region II, the exponent a of the MHS equation is lower than 0.5, the PVP chain approach the theta solvent behavior. Previous report has given value of a = 0.66 for PVP in water [25]. We note that the temperature don’t change the MHS exponent a; may be the range of chosen temperature is weak.

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T=10 C T=15 C 0,5 T=20 C T=25 C T=30 C 0 T=35 C T=40 C

-0,5 ] η

Ln[ -1

-1,5

-2

-2,5 9 9,5 10 10,5 11 11,5 12 12,5 13 Ln(Mw)

Fig. 4. Double-logarithmic plot of [η] [dL/g] against Mw and temperature for PVP in methanol.

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The rotational freedom of PVP monomer units around - C-C- single bonds can provide a less-flexible chain [10, 11, 15]. We have tried to adjust our curve, by the second-order least-squares regression [13]. This adjustment is presented in Fig. (5), for temperature equal to 20 °C, by the following equation: 2 Y = A0 + B0B X + C0 X (2)

Where, Y = ln [η] and X= ln (Mw). A0 is the intercept; B0B and C0 are the slope constants. These constants are summarized in Table 3 for several temperatures. The

B0B values of PVP in methanol are positive and slightly increase when the temperature increases. Inversely to B0B , C0 values are negative and slightly decrease. This behavior may be due to the increase in PVP-methanol interactions and decrease in PVP-PVP interactions [10, 11].

Tab. 3. Values of A0, B0B and C0 for Poly(vinyl-pyrrolidone) at different temperature estimated from the data least-squares regression, Eq. (2).

T °C A0 B0B C0 10 -15.260 2.510 -0.076 15 -17.450 2.660 -0.084 20 -17.260 2.820 -0.090 25 -16.480 2.650 -0.083 30 -16.000 2.510 -0.078 35 -18.200 2.750 -0.087 40 -19.530 2.950 -0.095

Synthetic polymer samples are usually polydisperse, and therefore, the molecular weights obtained with different techniques are different averages to which the scaling laws cannot be applied. The polydispersity affects the Mark-Houwink-Sakurada relationship since viscosity measures the “viscosity –average” molecular weight, Mη [15, 16]. This average is a function of the MHS exponent a of polymer and can be approximated by: 1/a 2 Mη / Mw = [(1 + a) Γ(1+ a)] (3) Where, Γ(a + 1) is the gamma function. Since in this case the exponent changes as a function of Mw, the a exponent may be estimated by a differentiating Eq. 2. a ≈ ∂ ln[η]/ ∂ ln(Mw) (4)

Tab. 4. Values of MHS exponents, a for all temperature and molecular weight estimated by a differentiating Eq. (2).

T °C a a a a Mw = 10 000 Mw = 24 000 Mw = 40 000 Mw = 360 000 10 1.12 1.00 0.92 0.59 15 1.11 0.97 0.88 0.51 20 1.16 1.00 0.91 0.52 25 1.12 0.98 0.89 0.53 30 1.07 0.94 0.86 0.51 35 1.14 0.98 0.90 0.51 40 1.20 1.03 0.94 0.52

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The approximate values of a against Mw are summarized in Table 4. The value of a is around 1 for all PVP molecular mass, except for 360 000. Apparently, PVP have more extended conformation for these firsts molecular masses. It is reasonable because the curvature of Eq. 2 is somewhat accentuated by the high molecular weight sample. A macromolecule can adopt many different conformations by rotation over the covalent single bonds that form the chain skeleton [11]. In most circumstances, the inter-conversion from one to another conformation is very easy, and the polymer changes among the allowed conformations.

The intrinsic viscosity data plotted against Mη are the open circles in Fig. 5. In fact we notice that there is a little difference between Mw and Mη especially for Mw = 360 000.

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Mw Mη 2

1 ] η Ln [

0

-1

-2 9 9,5 10 10,5 11 11,5 12 12,5 13 LLn(M)n(M)

Fig. 5. Correlation between intrinsic viscosity [η] and M for PVP in methanol solution, at T = 20 °C. The filled circles correspond to the Mw and the open circles correspond to the estimated Mη. The dashed line corresponds to the fit with the Eq. (2), with A0 =

-17.26, B0B = 2.820 and C0 = -0.090.

Experimental part

Dynamic light scattering Dynamic light scattering (DLS) is governed by the temporal autocorrelation function relative to the diffused light intensity. For small monodisperse particles undergoing Brownian diffusion, the expression of the autocorrelation function is:

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⎛ −t ⎞ ()= expAtg ⎜ ⎟ + B (5) ⎝ τ ⎠ B being the baseline and A representing the amplitude of the diffused intensity. The diffusion constants (A and B) can be determined by an adjustment of the autocorrelation function with the theoretical model. The parameter τ, is the autocorrelation time that gives information about the dynamic solution behavior and is related to the diffusion coefficient D by the following relation: 1 (6) D = q2τ 4πn θ The scattering vector q is given byq = sin , where n is the refractive index and θ λ 2 the diffusion angle. DLS measurements were carried out to determine the diffusion coefficient D for all PVP samples in methanol at 25 °C. The solutions were set into cylindrical light scattering cuvettes. To minimize stray light and regulate the sample temperature, the cell was centered in an index-matching bath with temperature control. The index fluid used was liquid paraffin. Temperature-control was pumped through a copper coil into the bath by a Haake K circulating bath. The temperature was controlled to ± 0.1 °C. Photon correlation spectroscopy was performed with a dynamic light scattering apparatus at 30° scattering angle using the green line (λ = 514.5 nm) of an argon ion laser (Cyonics, a division of uniphase - model 2201 - 65ML). Experiments were performed with a Malvern computing correlator (Multi 8 - type 7032 CE - system 4700 c) equipped with 256 channels. The beam passing through an attenuator then was focused into the scattering cell by a 300 mm focal length lens. A system comprising a lens and two pinholes excluded stray light scattered by the cell and focused the scattered light onto the PMT cathode (50 cps dark count at 1850 V). We measured the diffusion coefficient D for different concentrations in the chosen range. The concentration dependence of the apparent diffusion coefficient gives information about the interactions of the polymer with the solvent. The effect of the polymer concentration is considered by extrapolating the value of the apparent diffusion coefficient to zero concentration using the following equation:

Dapp= D0(1 + kDC) (7)

Where, kD is the dynamic virial coefficient and D0 is the diffusion coefficient at zero concentration. kD can be related to the thermodynamic properties of the polymer/solvent mixture according to the equation kD = 2A2M- ks- w, where ks is a 3 friction term defined as ks = k0(4πNA/3)Rh /M, w is the partial specific volume of the polymer in the solution, M is the molecular weight, A2 is the second virial coefficient and k0 a friction constant. This relationship is a result from linear irreversible thermodynamics [6] and has been tested in detail experimentally in dilute solutions by Brown and Zhou [26]. The first term (2A2M) in the expression for kD typically dominates in polymer solutions [26].

Viscosity Polymer solution intrinsic viscosity is an indicator of the average polymer coil size existing in solution. The classical Huggins equation when adapted to polymer-solvent system has the following form [27]:

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ηsp /C = [η] + bi C (8) where the interactions parameter, bi is related to the Huggins coefficient KH by bi = 2 KH[η] , and [η] is the intrinsic viscosity defined as

ηsp [η] = lim( ) (9) →0c C

ηsp, C represents the specific viscosity and the polymer concentration respectively.

For polymer dilute solutions, a plot of ηsp / C vs C should yield a straight line with intercept and slope respectively equal to [η] and bi. Theoretically, intrinsic viscosity [η] represents the effective hydrodynamic specific volume of an isolated polymer and interaction parameter; bi represents the interaction between polymer segments. The methanol was the solvent used for dynamic light scattering and viscosity measurements, and purified according to standard procedures. Methanol is a more polar solvent with higher viscosity, which may impede aggregation. The polymer mass concentrations C, was calculated from the weight fractions with the densities of solutions. These polymer solutions were purified by filtration through a Teflon membrane of 0.22 μm Millipore filters. Kinematics viscosities were measured using Ubbelohde capillary viscosimeter in a thermostatic bath (Schott Gerate Model CT 1450). The densities were measured with a Digital Precision Densimeter, DMA 46 (PAAR, Graz, Austria). The uncertainties in density measurements were about ± 0.1 mg/cm3. Only the experimental densities of solvent were corrected by linear regression, no corrections were made in presence of polymer. The temperature was measured by a quartz thermometer with accuracy about ± 2. 10-3 °C.

Conclusions By investigating the dynamic light scattering (DLS) and viscometric results of a polymer–solvent system we have shown that the Poly(vinyl pyrrolidone) in diluted regime behaves like a chain with excluded volume, with the exception of the viscosity results where we noticed a change of the conformation. The obtained results show that the viscosity is sensitive to the change of solvent quality i.e. the change of the polymeric chains conformation. In this case, the entire domain of molecular masses can be divided into two regions. These regions are separated by a crossover point that is manifested by plotting the variation of the intrinsic viscosity as a function of their molecular mass. In the molecular mass region below the crossover point (region I) the chains of polymer present a conformation of the appearance of excluded volume behavior. After this crossover point, there is a molecular mass region (region II) with a Θ-solvent behavior.

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