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Dynamic Surface Properties of Poly(vinylpyrrolidone) Solutions
Journal of Colloid and Interface Science 255, 417–424 (2002) doi:10.1006/jcis.2002.8614
Dynamic Surface Properties of Poly(vinylpyrrolidone) Solutions B. A. Noskov,∗ A. V. Akentiev,∗ and R. Miller†,1 ∗ Chemical Faculty, St. Petersburg State University, Univesitetskiy pr. 2, St. Petersburg-Stary Petergof, Russia; and †MPI f¨ur Kolloid und Grenzfl¨achenforschung, Am M¨uhlenberg 1, D-14476 Golm, Germany Received January 22, 2002; accepted July 16, 2002
The dynamic surface tension and the complex dynamic surface elasticity of poly(vinylpyrrolidone) (PVP) solutions were measured in the concentration range 10−5 wt% up to about 1 wt%. The surface tension changed slowly with time at low (<10−4 wt%) and high concentrations (>0.1 wt%). At low concentrations this is a consequence of the slow transport by diffusion of PVP molecules from the depth of the bulk phase to the surface. At high concentrations the time effect is unexpected and probably the result of PVP contamination of high surface activity. The dynamic surface elasticity of PVP solutions gradually decreases with increasing concentration up to the range of high concentrations (>0.1 wt%) where an abrupt increase in the elasticity caused by the adsorbed impurity is observed. At low and medium concentrations the viscoelastic behavior of PVP adsorbed films is similar to that of the previously investigated poly(ethylene oxide) and poly(ethylene glycol) films and is determined by the number of loops and tails protruding into the bulk phase. C 2002 Elsevier Science (USA) Key Words: polymer adsorption layers; surface viscoelasticity; competitive adsorption of impurities; adsorption kinetics.
INTRODUCTION
Dynamic properties of fluid interfaces are the object of extensive investigations. Obviously it is less the static surface tension that determines the behavior of foams and emulsions but rather dynamic and mechanical interfacial properties. The detailed description of various industrial and natural systems requires knowledge of the system response to a dilation of the liquid interface (1–3). If the interfacial deformations are small, this response is entirely characterized by a single fundamental surface property—the dilational dynamic surface elasticity (4). This parameter consists in general of two components characterizing, respectively, the elastic and dissipative properties of the surface layer and thus can be represented as a complex quantity. While the dynamic surface properties of solutions of conventional surfactants have been intensively studied for a long time (1, 5–7) and are mainly determined by the diffusional exchange of surfactant molecules between the bulk phase and the surface layer, any information on the dynamic surface properties of
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To whom correspondence should be addressed. 417
polymer solutions is scarce. Only spread polymer films at the liquid–gas interface have been studied relatively frequently, mainly by means of surface quasi-elastic light scattering (SQELS) (8–15). This experimental technique usually leads to reasonable values of the surface pressure and the real part of the dynamic surface elasticity, which are comparable with the results of other methods, but the sign of the imaginary component of the surface elasticity proves sometimes to be in contradiction with the second law of thermodynamics (7, 10, 11, 15). Buzza et al. showed that an effective two-dimensional negative viscosity could arise if the thickness of the polymer film approaches 1 micrometer (11). Such thickness is unreal for most systems and thus the difficulty in determining the surface viscosity probably indicates that the theory of the SQELS method is not completely adequate (4, 10, 15). The deviation of the transverse surface viscosity from zero in contradiction to the theory is another problem of this method (11). Moreover, the SQELS method can be applied only at high frequencies (≥10 Hz) while the main relaxation processes for polymer films usually correspond to the lower range of the spectrum (12, 16, 17) where other methods of mechanical relaxation spectrometry of surface layers must be used. Recent studies of the dynamic surface elasticity of poly (ethylene oxide) (PEO) and poly(ethylene glycol) (PEG) solutions in the frequency range of 0.1 Hz up to 1000 Hz showed rather unusual behavior (16, 17). Unlike for conventional surfactant solutions, the dilational surface elasticity of polymer solutions was rather low (≤10 mN/m) and decreased with increasing concentration over a broad concentration range. Only at the transition from dilute to semidilute solutions was an abrupt increase in the surface elasticity observed. Although the main features of this behavior are in agreement with the theory (19), only a tentative interpretation of the dilational viscoelasticity of PEO and PEG adsorption films was proposed (17, 18). In this work we apply low-frequency surface relaxation methods to solutions of a polymer of another chemical nature— poly(vinylpyrrolidone) (PVP). Although complexes of this substance formed with conventional surfactants in aqueous solutions is the subject of numerous studies (20, 21), the PVP adsorption films at the liquid–gas interface have been poorly investigated, probably because of experimental difficulties. For example, PVP is effectively invisible in the neutron reflection 0021-9797/02 $35.00
C 2002 Elsevier Science (USA)
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experiment (21). Huang and Wang applied the SQELS method to PVP solutions but did not try to determine the dynamic surface elasticity and discussed only the concentration dependence of the surface tension, in particular, a steep decrease in the surface tension at high concentrations (9). Recently Lou et al. measured the static and dynamic surface tensions of solutions of poly(vinylcaprolactam) (PV-CAP)—another polymeric cyclic amide (22). They also observed abrupt changes in the surface tension at high concentrations and unusually long time effects in this concentration range. The main aim of this work is to compare the concentration dependence of the dynamic surface elasticity of PVP solutions with the data for other polymers (17) and with recent theoretical results (19). To this end three experimental techniques have been applied: the method of transverse surface waves, the method of longitudinal surface waves, and the oscillating barrier method. First, the polymer adsorption layer model (19) is outlined. Then after a brief description of the experimental methods, the experimental results are presented and discussed.
DYNAMIC MODEL OF THE ADSORPTION LAYER
It is generally recognized now that adsorbed polymer films at the liquid–gas interface can be considered as consisting of two parts: a relatively narrow concentrated region contiguous to the gas phase (proximal region) and the region of tails and loops protruding into the bulk of the liquid where the global concentration of monomers is essentially lower (distal region). The relaxation of surface dilational stresses in this simple model was considered in Ref. (19), where three main additional assumptions were introduced. The first assumption is that the surface tension depends first of all on the monomer concentration in the proximal region and not on the concentration in the distal region. Then the relaxation of surface stresses to a surface dilation proceeds at the expense of drawing chains up to the surface or squeezing chains out of the surface (transitions of monomers between the proximal and distal regions). In the case of small deformations the departure of a polymer coil from the surface as a whole or the reverse process of entanglement of a free coil to the surface turn out to be very rare events and one can neglect their influence (second assumption). Finally, the motion of a tail or a loop in the distal region is assumed to be free from restrictions created by the neighboring loops and tails (third assumption). This is different from the case of the proximal region where polymer trains lying on the surface are restricted by entanglements with the neighboring trains. In this model the exchange of monomers between the proximal and distal regions under expansion (compression) of the surface can take place as a result of two processes: the relaxation of inner strains of a polymer chain or the drawing up (squeezing in) of the chain as a whole. The first process can be described mathematically by means of the solution of the corresponding boundary problem for the Rouse equation, while the second process can be considered in the framework of the two-dimensional reptation model by de Gennes.
These simple ideas can be elaborated further and lead to the following expression for the dynamic surface elasticity (19), 8iτB ω 23 ∂γ ε=− ∂ ln π p 2 π 2 (1 + iωτB / p 2 ) 23 iωτ2 , + 1− π 1 + iωτ2
[1]
where p changes from 1 to infinity and the sum includes only the odd terms, γ is the surface tension, ω is the angular frequency, is the number of moles of monomers per surface element of unit area in the proximal region, 3 is the number of moles of those monomers per unit area that belong to trains in the proximal region restricted by two loops or tails, τB is the relaxation time of the inner stresses of a polymer chain τB =
b2 N02 . 3π 2 kB T B
[2]
The relaxation time τ2 corresponds to the motion of a train in the proximal region as a single entity τ2 = −
N2 L 2 . B2 a(∂γ /∂)
[3]
2 is the number of moles of monomers per unit area in the proximal region that belong to trains restricted by a loop or tail only from one side (polymer tails lying on the surface), N2 is the mean number of monomers in such a train, N0 is the number of monomers inside the two-dimensional tube of entanglements, b is the statistical segment length, a is the mean distance between two neighboring entanglements forming the two-dimensional tube, B is the mobility constant, T is the temperature, and kB is the Boltzmann constant. If the concentration in the bulk phase tends to zero and the interaction of monomers with the surface is strong enough so that the adsorbed chains do not form loops and tails, then 2 tends to zero and τ2 to infinity. Then we have ε=−
∂γ ∂ ln
[4]
and the adsorbed film becomes purely elastic. The opposite case of high bulk concentration is more complicated. Here, the number of loops increases, τ2 and τB tend to zero and one can expect that the surface elasticity tends to zero too. However, the correctness of our third assumption becomes dubious in this case. It is more probable that the global reorganization of the surface layer structure under dilation leads to a small but finite dynamic surface elasticity (18). EXPERIMENTAL
The experimental setups for measurements of surface wave characteristics and surface tension oscillations in a Langmuir
DYNAMIC SURFACE PROPERTIES OF POLY(VINYLPYRROLIDONE) SOLUTIONS
trough together with the corresponding experimental procedures were described in detail elsewhere (6, 17, 18, 23, 24). We represent below only the basic principles of the employed experimental techniques. The characteristics of transverse capillary waves were measured by means of the electromechanical method based on the principle of a dynamic condenser (6, 17, 23). One condenser armature was a thin metal plate with the thickness less than half of the wavelength. The other armature was the liquid surface under investigation in a Teflon Langmuir trough. A mechanical generator excited the capillary waves. Propagation of the waves caused capacity oscillations of the dynamic condenser and as a result an alternating electric current appeared in the circuit. Measurements of the amplitude and phase of the electric signal allowed us to determine the damping coefficient and the length of transverse capillary waves. The longitudinal waves were created at the liquid surface in the Langmuir trough as a result of harmonical oscillations of a platinum wire (diameter of 0.1 mm) along the surface (17, 18, 24). The wire was immersed into the liquid parallel to its surface. Transverse capillary waves of higher frequency (180 Hz) propagating perpendicular to the longitudinal waves were used to detect the longitudinal oscillations of the surface layer. Propagation of longitudinal waves led to periodic changes of the surface tension and, consequently, to low-frequency oscillations of the wavelength of the transverse capillary waves. An optical wave probe was used to detect the transverse oscillations of the liquid surface. The alternating electric signal with the frequency of 180 Hz was monitored by a position-sensitive photodetector and was modulated by a lower frequency as a result of the propagation of longitudinal waves. A sensitive phase difference gauge allowed us to select the low-frequency component of the signal with the same frequency as the longitudinal waves and with amplitude proportional to the amplitude of these waves. Measurements of the changes in the phase and amplitude of the signal as a function of the distance between the platinum wire and the wave probe allowed us to determine the damping coefficient and the length of the longitudinal surface waves. If the frequency of oscillations of the mechanical barrier in a Langmuir trough is less than 0.2 Hz, the surface tension oscillations turn out to be homogeneous and the dilational elasticity can be determined directly by the oscillating barrier method (18). In this case the surface tension oscillations were measured by the Wilhelmy plate method with a roughened glass plate and the elasticity modulus was determined from the amplitude ratio of the oscillations of the surface tension and surface area. The phase shift between the oscillations of two measured parameters (surface tension and surface area) determines the phase angle of the dynamic surface elasticity. The same apparatus was employed for the measurements of the dynamic surface tension as a function of surface age. In this case a moving Teflon barrier was used to clean the surface in the Langmuir trough and to create a fresh surface of the solution under investigation. Each of the experimental setups was mounted on separate basements without mechanical connections to the building.
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PVP (Aldrich) with average molecular weights of M = 10000 (PVP10) and 55000 (PVP55) were used as received. Note that the surface properties of PVP solutions like PEO and PEG solutions (16, 17) proved to be almost independent of the polymer molecular weight and thus the estimation of molecular weight distribution was unimportant. All solutions were freshly prepared before each measurement and mixed carefully for about 15 min. Fresh twice-distilled water was used for this purpose. An all-Pyrex apparatus and alkaline permanganate were employed in the second stage of distillation. All measurements were carried out at 20.0 ± 0.5◦ C. RESULTS AND DISCUSSION
Figure 1 shows the surface tension of PVP10 and PVP55 solutions as a function of concentration c. At c < 0.1 wt% our data almost coincide with the results of Huang and Wang (9) for solutions of PVP with the molecular weight of 1000 K. However, in contrast to these authors, we did not observe any dependence of the static surface tension on the molecular weight in this concentration range. The agreement is somewhat worse at high concentrations (c > 0.1 wt%, especially for PVP10) where we observed more abrupt changes in the surface tension with concentration and slow changes with time (Fig. 2). Note that the points in Fig. 1 represent static values only for c < 0.1 wt%. At higher concentrations the figure shows only the dynamic surface tension at a surface age of about 500 min for PVP10 and more than 1200 min for PVP55. The attainment of the equilibrium surface tension is difficult because of the required long time. The abrupt surface tension drop in the range of relatively concentrated solutions (Fig. 1) is probably a general phenomenon and was observed for aqueous solutions of different polymers. For example, Lou et al. also described similar dependencies of the surface tension on time and concentration for PV-CAP
FIG. 1. Concentration dependence of the surface tension of PVP10 (open triangles) and PVP55 (solid squares) solutions. The arrow indicates the transition between the regions of static and dynamic values of the surface tension (see text).
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namic surface tension at short times (t → 0) (5), γ = γ0 − 2RT c0
FIG. 2. Kinetic dependence of the surface tension of PVP10 solutions at concentrations 1.12 wt% (squares) and 1.6 wt% (circles).
solutions (22). Earlier we observed also a similar concentration dependence for semidilute solutions of PEG and PEO (17). Slow changes of surface tension with time were observed at low concentrations (c < 2 × 10−4 wt%) too. Figure 3 shows as an example some results for PVP10 solutions. The surface tension decreases faster at least at c > 10−5 wt% than at high concentrations (c > 0.1 wt%), and the static values can be estimated with sufficient accuracy. Many authors studied the dynamic surface tension of polymer solutions at low concentrations and usually connected the time effects with slow diffusion of the polymer coils from the depth of the bulk phase to the interface followed by the adsorption, which can be sometimes accompanied by conformational transitions in the surface layer (5, 25–29). If the adsorption process is controlled by diffusion from the bulk phase, the following asymptotic relation holds for the dy-
FIG. 3. Kinetic dependence of the surface tension of PVP10 solutions at concentrations 0.00001 wt% (triangles) and 0.000059 wt% (circles). Curves are guides for the eye.
Dt , π
[5]
where γ0 is the surface tension of the solvent, R is the gas constant, c0 is the surfactant concentration in the bulk phase, and D is the surfactant diffusion coefficient. One must be extremely careful when applying Eq. [5] to nonequilibrium solutions of surface-active polymers where the surface tension can be determined not by the whole number of macromolecules at the interface but by the number of amphiphilic segments in the proximal region of the surface layer. Nevertheless, we used Eq. [5] for rough estimation of the PVP diffusion coefficient from the slope of the dependence of γ on t 1/2 . The results proved to be comparable with the data for conventional surfactants of low molecular weight and thus by about one order of magnitude higher as expected for polymers. This can indicate the influence of convection in the liquid of the Langmuir trough and means that the adsorption barrier and the conformational transition are not too significant for PVP adsorption. Thus the diffusion of polymer coils from the bulk phase can at least influence the adsorption rate. In this respect the system under investigation is similar to PEO solutions studied by Sauer and Yu (27). These authors used more exact calculations based on the comparison of adsorbed and spread surface films and proved the diffusion adsorption mechanism. While this interpretation of the time effects at low PVP concentrations is rather traditional, the time effects at high concentrations are new findings (22) and can hardly be explained in the same way. One can expect that the adsorption rate increases with concentration (5) and the equilibrium is reached beyond the time accessible for experimental observation in this study (t ≥ 10 s). Indeed, we did not observe any changes in the surface tension with time in the concentration range from 2 × 10−4 wt% up to 0.1 wt%. Slow changes in the structure of homopolymer surface films have been sometimes observed at the liquid–solid interface and have been connected with the substitution of shorter chains by longer macromolecules in the surface layer (30). Although this process can result in a subtle decrease in the system free energy, it cannot lead to noticeable changes in the surface tension. Indeed the surface tension is determined first of all by the monomer concentration in the proximal region (31) and cannot depend significantly on the length of the adsorbed macromolecules. Stronger effects could be expected if the macromolecules had some small parts of higher hydrophobicity. In this case the slow decrease in the surface tension could be explained by conformational transitions in the surface layer accompanied by the increase in adsorption of more hydrophobic segments. The latter process can lead to formation of a quasibrush structure at high concentrations. However, this mechanism is more probable for block copolymer solutions and is hardly possible for the system under investigation.
DYNAMIC SURFACE PROPERTIES OF POLY(VINYLPYRROLIDONE) SOLUTIONS
Kim and Cao assumed that the change in solvent quality in the surface layer of relatively concentrated aqueous PEO solutions could lead to surface aggregation and to additional reduction of the surface tension (32). However, to the best of our knowledge there are no data indicating similar changes of the solvent quality for PVP solutions. Besides, slow time effects have not been discovered for PEO solutions, thus indicating the significant difference between these two systems. It is more probable that anomalous behavior of surface properties at high PVP concentrations is caused by traces of impurities of high surface activity. It is well known that their influence can be overwhelming in studies of adsorption kinetics (6, 33–36). Enormous efforts have been directed to elucidate the role of impurities and to minimize their effects. To the best of our knowledge the polymer adsorption films have not been investigated yet in this respect. Figure 1 shows that the equilibrium surface pressure of PVP is rather low (about 3 mN/m) in a broad concentration range. This means that if the surface activity of a substance is high, even small traces can be sufficient in order to exceed the PVP surface pressure. In this case the impurity will displace the polymer from the surface layer. The displacement of polymers including proteins by conventional surfactants has been extensively studied for the last few years (37–40). Note that the chemical nature of the admixture is not known in our case. This can be, for example, a scarcely soluble surfactant or a polymer. It is only important that its concentration is extremely low and the surface activity is high. At low and moderate PVP concentrations the total admixture concentration is insufficient to create a surface pressure that exceeds 3 mN/m. While the PVP surface pressure is almost independent of concentration (Fig. 1), the impurity equilibrium surface pressure can increase with concentration and at about c > 0.1 wt% for PVP10 and at c > 0.5 wt% for PVP55 exceeds this threshold. Then PVP is gradually displaced from the surface by the slowly adsorbing impurity (Fig. 2). At small admixture concentrations, its adsorption rate can be extremely slow (33–36). To check out the proposed mechanism of slow processes observed at high PVP concentrations and to elucidate the role of impurities we used the method of Lunkenheimer and Miller and subjected the adsorbed surface film to expansion and subsequent contraction in the Langmuir trough during the equilibration (34). If this procedure was carried out within a few minutes after the formation of the fresh interface, the amplitude of the surface tension change was relatively low and the final value was close to the surface tension before the contraction. However, if the surface contraction and expansion were repeated in a few hours when one can expect the accumulation of the impurity in the surface layer, the amplitude was significantly larger and the final surface tension value exceeded significantly the value before the contraction. The latter results are typical for systems containing a slowly adsorbing (desorbing) impurity (33, 34) and were not observed at lower PVP concentrations where the influence of impurities was significantly weaker. Indeed the contraction is followed by impurity desorption, which leads to large losses of the impurity in the surface layer. The
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FIG. 4. Concentration dependence of εr (solid symbols) and εi (open symbols) of PVP10 and PVP55 (crosses) solutions at frequencies of 0.05 Hz (squares), 0.5 Hz (triangles, crosses), and 270 Hz (circles).
subsequent expansion does not compensate for this loss because of the slow admixture adsorption, and the surface tension does not return to the value preceding contraction. Note that it is hardly possible to explain all the observed time effects if one assumes only the possibility of conformational transitions in the surface layer without any influence of the admixture desorption– adsorption. Our data on the dynamic surface elasticity of PVP solutions (Fig. 4) also confirm this interpretation. At c < 0.1 wt% for PVP10 and at c < 0.2 wt% for PVP55 both components of the surface elasticity are typical for solutions of nonionic polymers (16, 17) and do not exceed 6 mN/m, while at higher concentrations the surface elasticity increases by several times and becomes comparable with values for solutions of conventional surfactants (1, 7, 23). The problem of the admixture chemical nature in PVP solutions is beyond the scope of this work. Even for solutions of conventional surfactants this chemical problem would be difficult to solve. For polymer systems it can be significantly more complicated. Thus only the results of this work at low and medium concentrations (c < 0.1 wt% for PVP10 and at c < 0.2 wt% for PVP55) correspond more or less to a pure PVP adsorption film. At higher concentrations an admixture probably determines the surface properties. The admixture concentration for PVP10 is probably higher than that for PVP55, which leads to the more extended range of the constant surface properties for solutions of the latter polymer. To study this problem further we measured the dynamic surface elasticity. The dynamic surface elasticity ε in the frequency range from 0.007 Hz up to 0.11 Hz was determined by the oscillating barrier method. The sinusoidal oscillations of the area A of the liquid surface in the Langmuir trough generate oscillations of the surface tension measured by the Wilhelmy plate. Both periodical functions of time γ (t) = γ (0) + δγ (t) and A(t) = A(0) + δ A(t) can be represented in the complex form, and the complex surface
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elasticity at the given angular frequency can be determined as a ratio, ε(ω) = δγ /δ ln A.
[6]
At higher frequencies the dynamic surface elasticity was calculated from the measured characteristics of longitudinal surface waves (in the frequency range from 0.2 Hz up to 3 Hz) or transverse capillary waves (at higher frequencies up to 520 Hz). The dependence of the length of transverse surface waves on concentration is determined by the surface tension and as a result the corresponding dependence for PVP solutions resembles the curve in Fig. 1. The concentration dependence of the damping coefficient α is mainly determined by the surface elasticity and turns out to be more complicated. Figure 5 shows as an example the dependence α(c) for solutions of PVP10 at a frequency of 200 Hz. Similar curves were obtained for other frequencies and for PVP55 solutions too. The results in Fig. 5 are typical for polymer solutions and differ from the α(c) dependences for conventional surfactants by significantly slower changes in concentration and by lower values of the damping in the region of the local minimum (16, 17). This indicates lower values of the dynamic surface elasticity and its more gradual change with concentration in the former case. For more careful investigation of the dynamic surface properties both the real εr and the imaginary εi components of the dynamic surface elasticity were calculated from the characteristics of transverse and longitudinal surface waves according to the dispersion relation (17) ε˜ = ε˜ r + ε˜ i =
ρω2 [ρω2 − (σ k 3 +ρgk) tanh(kh)] + 4iρµω3 k 2 + 4µ2 ω2 k 3 [m tanh(kh) − k] , mk 2 [ρω2 − (σ k 3 + ρgk) tanh(kh)] + k 3 (σ k 3 +ρgk)
[7]
FIG. 6. Frequency dependence of εr (solid symbols) and εi (open symbols) of PVP10 solutions at concentrations 0.004 wt% (squares) and 0.000105 wt% (triangles).
wavelength, m 2 = k 2 − iωρ/µ, Re[m] > 0, ρ is the density of the subphase, µ is the shear viscosity of the subphase, g is the gravitational acceleration, and h is the depth of the liquid (in our setup h equals 15 mm). Figures 6 and 7 show some examples of the frequency dependence of both components of the surface viscoelasticity for PVP10 and PVP55 solutions at different concentrations. It has been shown recently that the characteristic time of the relaxation process in PEG adsorbed films equals 0.06 s (16, 17). All results for PVP solutions including those in Figs. 6 and 7 give no distinct evidence of any relaxation processes in the frequency range from 0.007 Hz up to 520 Hz. However, this can only be a consequence of the low dynamic surface elasticity. Indeed in the concentration range from 0.0001 wt% up to 0.1 wt% the real
where k = 2π/λ + iα is the complex wave number, λ is the
FIG. 5. Concentration dependence of the damping coefficient of transverse capillary waves for PVP10 solutions.
FIG. 7. Frequency dependence of εr (solid symbols) and εi (open symbols) of PVP55 solutions at concentrations 0.00003 wt% (triangles) and 0.01 wt% (squares).
DYNAMIC SURFACE PROPERTIES OF POLY(VINYLPYRROLIDONE) SOLUTIONS
part of the elasticity changed only from 1 mN/m up to 5 mN/m and the imaginary part from 0 up to 2 mN/m, and only in the limiting cases at low and high concentrations were these values exceeded. Thus any frequency changes in the elasticity could lie within the error limits, which are about ±0.5 and ±1 mN/m for εr and εi , respectively, in the medium concentration range. Figure 4 shows the concentration dependence of the dynamic surface elasticity for solutions of PVP10 and PVP55 for different frequencies. One can see again that the surface elasticity is almost independent of frequency but the concentration dependence of the real component at least is distinct enough. The abrupt increase in the elasticity at high concentrations (c > 0.1 wt% for PVP10 and at c > 0.2 wt% for PVP55) can be a consequence of the displacement of PVP from the surface layer by a stronger surface-active admixture. High values of the elasticity in this concentration range can indicate the nonpolymeric nature of the impurity. Although no equilibrium adsorption films were obtained in this concentration range, the measured values of εr and εi are probably close to the equilibrium because the surface elasticities do not change in the error limits during the final steps of the equilibration. At lower concentrations PVP chains in the surface layer determine the surface viscoelastic properties. One can see that εr gradually decreases from about 5 mN/m to about 1 mN/m for both polymers when the concentration increases up to 0.01 wt%. This decrease in the elasticity was obtained for PEG and PEO solutions too and is probably typical for solutions of nonionic linear flexible polymers (16, 17). At concentrations lower than about 3 × 10−5 wt% the equilibration process requires too much time and only the elasticity of the system far from equilibrium can be measured. One can assume that the elasticity goes through a maximum when the PVP concentration is changed from zero to 3 × 10−5 wt%. Measuring the time dependence of the surface elasticity can check this conclusion. Indeed a gradual increase in the PVP adsorption will lead to changes in the surface concentration from zero to the equilibrium value. A maximum of the real component of surface elasticity can be indeed observed in Fig. 8 where both components are plotted as a function of time for c = 3 × 10−5 wt%. The maximum of εr is about 6 mN/m, which obviously must correspond to an equilibrium bulk concentration much lower than 3 × 10−5 wt%. The decrease in the dynamic surface elasticity with increasing concentration at a given frequency of perturbations is also sometimes observed for solutions of conventional surfactants of low molecular weight (23, 24). However, in that case the rate of the decrease is significantly higher, which can be easily explained by the fast decrease in the diffusion relaxation time for surfactants with increasing concentration. When this characteristic time approaches the period of perturbations the dynamic surface elasticity begins to drop. Figure 4 shows that this explanation cannot be used for polymer solutions, where the decrease of εr is significantly slower and does not depend on the frequency in the broad frequency range from 0.007 Hz up to 520 Hz. For most of the frequencies and concentrations under investigation
423
FIG. 8. Kinetic dependence of εr (solid symbols) and εi (open symbols) of PVP55 solutions at concentration 0.00003 wt%.
the period of perturbations exceeds the characteristic diffusion time. The similarity between the surface viscoelastic properties of PVP solutions and PEG and PEO solutions allows us to use the dynamic model (17, 19), as outlined above, also for PVP. At low concentrations the PVP chains are unfolded and lie almost entirely in the proximal region of the surface layer without loops and tails protruding into the adjacent bulk phase (pancake conformation). In this case the film is purely elastic at frequencies under investigation and Eq. [4] holds. This concentration range expands approximately up to the region of the elasticity maximum. At higher concentrations the chains cannot unfold in the surface layer during the adsorption process completely, which leads to the formation of loops and tails in the proximal region. The mechanical stresses in the surface layer can be now relaxed at the expense of the monomer exchange between two regions of the surface layer. The monomers are squeezed into the region of loops and tails upon compression or drawn into the proximal region upon expansion. If the period of perturbations is comparable with the corresponding relaxation time the surface film becomes viscoelastic (17–19). The information on the structure of the adsorbed PVP films studied in this work is insufficient for calculations of the dynamic surface elasticity from Eq. [1]. On the other hand, the region of the elasticity maximum corresponds to very low PVP bulk concentrations, which can be investigated only as transient states during the equilibration process (Fig. 8). When we measured the dynamic surface elasticity using small perturbations of the equilibrium state, the obtained values were too low for a determination of the relaxation times (Fig. 4). Here we can use only the similarity between the adsorbed films of PVP and PEG and assume that the relaxation times for PVP are also comparable with the periods of perturbations used in this work, at least at concentrations just above the region of the elasticity maximum. The decrease in the dynamic surface elasticity with concentration can probably give some grounds for this point of view.
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CONCLUSIONS
The results on the dynamic surface tension and dynamic surface elasticity of PVP adsorbed films have shown that an impurity gradually displaces PVP chains from the surface at concentrations higher than 0.1 wt% and thus leads to slow equilibration of the system. Only in the range of low and middle concentrations does the adsorption of PVP chains determine the surface properties. At concentrations lower than 0.1 wt% the dynamic surface elasticity gradually decreases when PVP is added to the solution. This behavior is similar to that of solutions of PEO and PEG. Although the relaxation time was not determined for PVP solutions, we consider that the decrease in the elasticity is a consequence of the increase in the number of loops and tails in the distal region of the surface layer. ACKNOWLEDGMENTS This work was financially supported by the Russian Foundation of Fundamental Research (Project RFFI 99-03-32247a). A.V.A. is grateful to INTAS for the fellowship grant for young scientists (YSF 00-166).
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Langevin, D., Curr. Opinion Colloid Interface Sci. 3, 600 (1998). Langevin, D., Adv. Colloid Interface Sci. 88, 209 (2000). Wilde, P. J., Curr. Opinion Colloid Interface Sci. 5, 176 (2000). Noskov, B. A., and Loglio, G., Colloid Surf. A 143, 167 (1998). Dukhin, S. S., Kretzschmar, G., and Miller, R., in “Studies in Interface Science” (D. M¨obius and R. Miller Eds.), Vol. 1. Elsevier, Amsterdam, 1995. Noskov, B. A., Adv. Colloid Interface Sci. 69, 63 (1996). Noskov, B. A., Adv. Colloid Interface Sci. 95, 237 (2002). Sauer, B. B., Kawaguchi, M., and Yu, H., Macromolecules 20, 2732 (1987). Huang, Q. R., and Wang, G. H., J. Chem. Phys. 105, 6546 (1996). Peace, S. K., Richards, R. W., and Williams, N., Langmuir 14, 667 (1998). Buzza, D. M. A., Jones, J. L., McLeish, T. C. B., and Richards, R. W., J. Chem. Phys. 109, 5008 (1998).
12. Monroy, F., Ortega, F., and Rubio, R. G., Phys. Rev. E 58, 7629 (1998). 13. Monroy, F., Ortega, F., and Rubio, R. G., J. Phys. Chem. B 103, 2061 (1999). 14. Esker, A. R., Zhang, L.-H., Sauer, B. B., Lee, W., and Yu, H., Colloids Surf. A 171, 131 (2000). 15. Milling, A. J., Richards, R. W., Hiorns, R. C., and Jones, R. G., Macromolecules 33, 2651 (2000). 16. Noskov, B. A., Akentiev, A. V., Alexandrov, D. A., Loglio, G., and Miller, R., Mendeleev Commun. N5, 190 (1998). 17. Noskov, B. A., Akentiev, A. V., Loglio, G., and Miller, R., J. Phys. Chem. B 104, 7923 (2000). 18. Akentiev, A. V., and Noskov, B. A., Colloid J. 64, 129 (2002). 19. Noskov, B. A., Colloid Polym. Sci. 273, 263 (1995). 20. Chari, K., and Hossain, T., J. Phys. Chem. 95, 3302 (1991). 21. Purcell, I. P., Lu, J. R., Thomas, R. K., Howe, A. M., and Penfold, J., Langmuir 14, 1637 (1998). 22. Lou, A., Pethica, B. A., and Somasundaran, P., Langmuir 16, 7691 (2000). 23. Noskov, B. A., and Grigoriev, D. O., Langmuir 12, 3399 (1996). 24. Noskov, B. A., Alexandrov, D. A., and Miller, R., J. Colloid Interface Sci. 219, 250 (1999). 25. Glass, J. E., J. Phys. Chem. 72, 4459 (1968). 26. Lankveld, J. M. G., and Lyklema, J., J. Colloid Interface Sci. 41, 454 (1972). 27. Sauer, B. B., and Yu, H., Macromolecules 22, 786 (1989). 28. Nahringbauer, I., J. Colloid Interface Sci. 176, 318 (1995). 29. Zhang, J., and Pelton, R., Langmuir 15, 5662 (1999). 30. Douglas, J. F., Schneider, H. M., Frantz, P., Lipman, R., and Granick, S., J. Phys. Condens. Matter 9, 7699 (1997). 31. Barentine, C., and Joanny, J. F., Langmuir 15, 1802 (1999). 32. Kim, M. B., and Kao, B. H., Europhys. Lett. 24, 229 (1993). 33. Mysels, K. J., and Florence, A. T., J. Colloid Interface Sci. 43, 577 (1973). 34. Lunkenheimer, K., and Miller, R., Tenside 16, 6 (1979). 35. Lunkenheimer, K., Miller, R., and Fruhner, H., Colloid Polym. Sci. 269, 599 (1982). 36. Mysels, K. J., Langmuir 2, 423 (1986). 37. Cook, D. J., Blondel, J. A. K., Lu, J., Thomas, R. K., Simister, E. A., and Penfold, J., Langmuir 14, 1990 (1998). 38. Cook, D. J., Dong, C. C., Lu, J., Thomas, R. K., Simister, E. A., and Penfold, J., J. Phys. Chem. B 102, 4912 (1998). 39. Jean, B., Lee, L.-T., and Cabane, B., Langmuir 15, 7590 (1999). 40. Mackie, A. R., Gunning, A. P., Wilde, P. J., and Morris, V. J., J. Colloid Interface Sci. 210, 157 (1999).
Dynamic Surface Properties of Poly(vinylpyrrolidone) Solutions B. A. Noskov,∗ A. V. Akentiev,∗ and R. Miller†,1 ∗ Chemical Faculty, St. Petersburg State University, Univesitetskiy pr. 2, St. Petersburg-Stary Petergof, Russia; and †MPI f¨ur Kolloid und Grenzfl¨achenforschung, Am M¨uhlenberg 1, D-14476 Golm, Germany Received January 22, 2002; accepted July 16, 2002
The dynamic surface tension and the complex dynamic surface elasticity of poly(vinylpyrrolidone) (PVP) solutions were measured in the concentration range 10−5 wt% up to about 1 wt%. The surface tension changed slowly with time at low (<10−4 wt%) and high concentrations (>0.1 wt%). At low concentrations this is a consequence of the slow transport by diffusion of PVP molecules from the depth of the bulk phase to the surface. At high concentrations the time effect is unexpected and probably the result of PVP contamination of high surface activity. The dynamic surface elasticity of PVP solutions gradually decreases with increasing concentration up to the range of high concentrations (>0.1 wt%) where an abrupt increase in the elasticity caused by the adsorbed impurity is observed. At low and medium concentrations the viscoelastic behavior of PVP adsorbed films is similar to that of the previously investigated poly(ethylene oxide) and poly(ethylene glycol) films and is determined by the number of loops and tails protruding into the bulk phase. C 2002 Elsevier Science (USA) Key Words: polymer adsorption layers; surface viscoelasticity; competitive adsorption of impurities; adsorption kinetics.
INTRODUCTION
Dynamic properties of fluid interfaces are the object of extensive investigations. Obviously it is less the static surface tension that determines the behavior of foams and emulsions but rather dynamic and mechanical interfacial properties. The detailed description of various industrial and natural systems requires knowledge of the system response to a dilation of the liquid interface (1–3). If the interfacial deformations are small, this response is entirely characterized by a single fundamental surface property—the dilational dynamic surface elasticity (4). This parameter consists in general of two components characterizing, respectively, the elastic and dissipative properties of the surface layer and thus can be represented as a complex quantity. While the dynamic surface properties of solutions of conventional surfactants have been intensively studied for a long time (1, 5–7) and are mainly determined by the diffusional exchange of surfactant molecules between the bulk phase and the surface layer, any information on the dynamic surface properties of
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To whom correspondence should be addressed. 417
polymer solutions is scarce. Only spread polymer films at the liquid–gas interface have been studied relatively frequently, mainly by means of surface quasi-elastic light scattering (SQELS) (8–15). This experimental technique usually leads to reasonable values of the surface pressure and the real part of the dynamic surface elasticity, which are comparable with the results of other methods, but the sign of the imaginary component of the surface elasticity proves sometimes to be in contradiction with the second law of thermodynamics (7, 10, 11, 15). Buzza et al. showed that an effective two-dimensional negative viscosity could arise if the thickness of the polymer film approaches 1 micrometer (11). Such thickness is unreal for most systems and thus the difficulty in determining the surface viscosity probably indicates that the theory of the SQELS method is not completely adequate (4, 10, 15). The deviation of the transverse surface viscosity from zero in contradiction to the theory is another problem of this method (11). Moreover, the SQELS method can be applied only at high frequencies (≥10 Hz) while the main relaxation processes for polymer films usually correspond to the lower range of the spectrum (12, 16, 17) where other methods of mechanical relaxation spectrometry of surface layers must be used. Recent studies of the dynamic surface elasticity of poly (ethylene oxide) (PEO) and poly(ethylene glycol) (PEG) solutions in the frequency range of 0.1 Hz up to 1000 Hz showed rather unusual behavior (16, 17). Unlike for conventional surfactant solutions, the dilational surface elasticity of polymer solutions was rather low (≤10 mN/m) and decreased with increasing concentration over a broad concentration range. Only at the transition from dilute to semidilute solutions was an abrupt increase in the surface elasticity observed. Although the main features of this behavior are in agreement with the theory (19), only a tentative interpretation of the dilational viscoelasticity of PEO and PEG adsorption films was proposed (17, 18). In this work we apply low-frequency surface relaxation methods to solutions of a polymer of another chemical nature— poly(vinylpyrrolidone) (PVP). Although complexes of this substance formed with conventional surfactants in aqueous solutions is the subject of numerous studies (20, 21), the PVP adsorption films at the liquid–gas interface have been poorly investigated, probably because of experimental difficulties. For example, PVP is effectively invisible in the neutron reflection 0021-9797/02 $35.00
C 2002 Elsevier Science (USA)
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experiment (21). Huang and Wang applied the SQELS method to PVP solutions but did not try to determine the dynamic surface elasticity and discussed only the concentration dependence of the surface tension, in particular, a steep decrease in the surface tension at high concentrations (9). Recently Lou et al. measured the static and dynamic surface tensions of solutions of poly(vinylcaprolactam) (PV-CAP)—another polymeric cyclic amide (22). They also observed abrupt changes in the surface tension at high concentrations and unusually long time effects in this concentration range. The main aim of this work is to compare the concentration dependence of the dynamic surface elasticity of PVP solutions with the data for other polymers (17) and with recent theoretical results (19). To this end three experimental techniques have been applied: the method of transverse surface waves, the method of longitudinal surface waves, and the oscillating barrier method. First, the polymer adsorption layer model (19) is outlined. Then after a brief description of the experimental methods, the experimental results are presented and discussed.
DYNAMIC MODEL OF THE ADSORPTION LAYER
It is generally recognized now that adsorbed polymer films at the liquid–gas interface can be considered as consisting of two parts: a relatively narrow concentrated region contiguous to the gas phase (proximal region) and the region of tails and loops protruding into the bulk of the liquid where the global concentration of monomers is essentially lower (distal region). The relaxation of surface dilational stresses in this simple model was considered in Ref. (19), where three main additional assumptions were introduced. The first assumption is that the surface tension depends first of all on the monomer concentration in the proximal region and not on the concentration in the distal region. Then the relaxation of surface stresses to a surface dilation proceeds at the expense of drawing chains up to the surface or squeezing chains out of the surface (transitions of monomers between the proximal and distal regions). In the case of small deformations the departure of a polymer coil from the surface as a whole or the reverse process of entanglement of a free coil to the surface turn out to be very rare events and one can neglect their influence (second assumption). Finally, the motion of a tail or a loop in the distal region is assumed to be free from restrictions created by the neighboring loops and tails (third assumption). This is different from the case of the proximal region where polymer trains lying on the surface are restricted by entanglements with the neighboring trains. In this model the exchange of monomers between the proximal and distal regions under expansion (compression) of the surface can take place as a result of two processes: the relaxation of inner strains of a polymer chain or the drawing up (squeezing in) of the chain as a whole. The first process can be described mathematically by means of the solution of the corresponding boundary problem for the Rouse equation, while the second process can be considered in the framework of the two-dimensional reptation model by de Gennes.
These simple ideas can be elaborated further and lead to the following expression for the dynamic surface elasticity (19), 8iτB ω 23 ∂γ ε=− ∂ ln π p 2 π 2 (1 + iωτB / p 2 ) 23 iωτ2 , + 1− π 1 + iωτ2
[1]
where p changes from 1 to infinity and the sum includes only the odd terms, γ is the surface tension, ω is the angular frequency, is the number of moles of monomers per surface element of unit area in the proximal region, 3 is the number of moles of those monomers per unit area that belong to trains in the proximal region restricted by two loops or tails, τB is the relaxation time of the inner stresses of a polymer chain τB =
b2 N02 . 3π 2 kB T B
[2]
The relaxation time τ2 corresponds to the motion of a train in the proximal region as a single entity τ2 = −
N2 L 2 . B2 a(∂γ /∂)
[3]
2 is the number of moles of monomers per unit area in the proximal region that belong to trains restricted by a loop or tail only from one side (polymer tails lying on the surface), N2 is the mean number of monomers in such a train, N0 is the number of monomers inside the two-dimensional tube of entanglements, b is the statistical segment length, a is the mean distance between two neighboring entanglements forming the two-dimensional tube, B is the mobility constant, T is the temperature, and kB is the Boltzmann constant. If the concentration in the bulk phase tends to zero and the interaction of monomers with the surface is strong enough so that the adsorbed chains do not form loops and tails, then 2 tends to zero and τ2 to infinity. Then we have ε=−
∂γ ∂ ln
[4]
and the adsorbed film becomes purely elastic. The opposite case of high bulk concentration is more complicated. Here, the number of loops increases, τ2 and τB tend to zero and one can expect that the surface elasticity tends to zero too. However, the correctness of our third assumption becomes dubious in this case. It is more probable that the global reorganization of the surface layer structure under dilation leads to a small but finite dynamic surface elasticity (18). EXPERIMENTAL
The experimental setups for measurements of surface wave characteristics and surface tension oscillations in a Langmuir
DYNAMIC SURFACE PROPERTIES OF POLY(VINYLPYRROLIDONE) SOLUTIONS
trough together with the corresponding experimental procedures were described in detail elsewhere (6, 17, 18, 23, 24). We represent below only the basic principles of the employed experimental techniques. The characteristics of transverse capillary waves were measured by means of the electromechanical method based on the principle of a dynamic condenser (6, 17, 23). One condenser armature was a thin metal plate with the thickness less than half of the wavelength. The other armature was the liquid surface under investigation in a Teflon Langmuir trough. A mechanical generator excited the capillary waves. Propagation of the waves caused capacity oscillations of the dynamic condenser and as a result an alternating electric current appeared in the circuit. Measurements of the amplitude and phase of the electric signal allowed us to determine the damping coefficient and the length of transverse capillary waves. The longitudinal waves were created at the liquid surface in the Langmuir trough as a result of harmonical oscillations of a platinum wire (diameter of 0.1 mm) along the surface (17, 18, 24). The wire was immersed into the liquid parallel to its surface. Transverse capillary waves of higher frequency (180 Hz) propagating perpendicular to the longitudinal waves were used to detect the longitudinal oscillations of the surface layer. Propagation of longitudinal waves led to periodic changes of the surface tension and, consequently, to low-frequency oscillations of the wavelength of the transverse capillary waves. An optical wave probe was used to detect the transverse oscillations of the liquid surface. The alternating electric signal with the frequency of 180 Hz was monitored by a position-sensitive photodetector and was modulated by a lower frequency as a result of the propagation of longitudinal waves. A sensitive phase difference gauge allowed us to select the low-frequency component of the signal with the same frequency as the longitudinal waves and with amplitude proportional to the amplitude of these waves. Measurements of the changes in the phase and amplitude of the signal as a function of the distance between the platinum wire and the wave probe allowed us to determine the damping coefficient and the length of the longitudinal surface waves. If the frequency of oscillations of the mechanical barrier in a Langmuir trough is less than 0.2 Hz, the surface tension oscillations turn out to be homogeneous and the dilational elasticity can be determined directly by the oscillating barrier method (18). In this case the surface tension oscillations were measured by the Wilhelmy plate method with a roughened glass plate and the elasticity modulus was determined from the amplitude ratio of the oscillations of the surface tension and surface area. The phase shift between the oscillations of two measured parameters (surface tension and surface area) determines the phase angle of the dynamic surface elasticity. The same apparatus was employed for the measurements of the dynamic surface tension as a function of surface age. In this case a moving Teflon barrier was used to clean the surface in the Langmuir trough and to create a fresh surface of the solution under investigation. Each of the experimental setups was mounted on separate basements without mechanical connections to the building.
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PVP (Aldrich) with average molecular weights of M = 10000 (PVP10) and 55000 (PVP55) were used as received. Note that the surface properties of PVP solutions like PEO and PEG solutions (16, 17) proved to be almost independent of the polymer molecular weight and thus the estimation of molecular weight distribution was unimportant. All solutions were freshly prepared before each measurement and mixed carefully for about 15 min. Fresh twice-distilled water was used for this purpose. An all-Pyrex apparatus and alkaline permanganate were employed in the second stage of distillation. All measurements were carried out at 20.0 ± 0.5◦ C. RESULTS AND DISCUSSION
Figure 1 shows the surface tension of PVP10 and PVP55 solutions as a function of concentration c. At c < 0.1 wt% our data almost coincide with the results of Huang and Wang (9) for solutions of PVP with the molecular weight of 1000 K. However, in contrast to these authors, we did not observe any dependence of the static surface tension on the molecular weight in this concentration range. The agreement is somewhat worse at high concentrations (c > 0.1 wt%, especially for PVP10) where we observed more abrupt changes in the surface tension with concentration and slow changes with time (Fig. 2). Note that the points in Fig. 1 represent static values only for c < 0.1 wt%. At higher concentrations the figure shows only the dynamic surface tension at a surface age of about 500 min for PVP10 and more than 1200 min for PVP55. The attainment of the equilibrium surface tension is difficult because of the required long time. The abrupt surface tension drop in the range of relatively concentrated solutions (Fig. 1) is probably a general phenomenon and was observed for aqueous solutions of different polymers. For example, Lou et al. also described similar dependencies of the surface tension on time and concentration for PV-CAP
FIG. 1. Concentration dependence of the surface tension of PVP10 (open triangles) and PVP55 (solid squares) solutions. The arrow indicates the transition between the regions of static and dynamic values of the surface tension (see text).
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namic surface tension at short times (t → 0) (5), γ = γ0 − 2RT c0
FIG. 2. Kinetic dependence of the surface tension of PVP10 solutions at concentrations 1.12 wt% (squares) and 1.6 wt% (circles).
solutions (22). Earlier we observed also a similar concentration dependence for semidilute solutions of PEG and PEO (17). Slow changes of surface tension with time were observed at low concentrations (c < 2 × 10−4 wt%) too. Figure 3 shows as an example some results for PVP10 solutions. The surface tension decreases faster at least at c > 10−5 wt% than at high concentrations (c > 0.1 wt%), and the static values can be estimated with sufficient accuracy. Many authors studied the dynamic surface tension of polymer solutions at low concentrations and usually connected the time effects with slow diffusion of the polymer coils from the depth of the bulk phase to the interface followed by the adsorption, which can be sometimes accompanied by conformational transitions in the surface layer (5, 25–29). If the adsorption process is controlled by diffusion from the bulk phase, the following asymptotic relation holds for the dy-
FIG. 3. Kinetic dependence of the surface tension of PVP10 solutions at concentrations 0.00001 wt% (triangles) and 0.000059 wt% (circles). Curves are guides for the eye.
Dt , π
[5]
where γ0 is the surface tension of the solvent, R is the gas constant, c0 is the surfactant concentration in the bulk phase, and D is the surfactant diffusion coefficient. One must be extremely careful when applying Eq. [5] to nonequilibrium solutions of surface-active polymers where the surface tension can be determined not by the whole number of macromolecules at the interface but by the number of amphiphilic segments in the proximal region of the surface layer. Nevertheless, we used Eq. [5] for rough estimation of the PVP diffusion coefficient from the slope of the dependence of γ on t 1/2 . The results proved to be comparable with the data for conventional surfactants of low molecular weight and thus by about one order of magnitude higher as expected for polymers. This can indicate the influence of convection in the liquid of the Langmuir trough and means that the adsorption barrier and the conformational transition are not too significant for PVP adsorption. Thus the diffusion of polymer coils from the bulk phase can at least influence the adsorption rate. In this respect the system under investigation is similar to PEO solutions studied by Sauer and Yu (27). These authors used more exact calculations based on the comparison of adsorbed and spread surface films and proved the diffusion adsorption mechanism. While this interpretation of the time effects at low PVP concentrations is rather traditional, the time effects at high concentrations are new findings (22) and can hardly be explained in the same way. One can expect that the adsorption rate increases with concentration (5) and the equilibrium is reached beyond the time accessible for experimental observation in this study (t ≥ 10 s). Indeed, we did not observe any changes in the surface tension with time in the concentration range from 2 × 10−4 wt% up to 0.1 wt%. Slow changes in the structure of homopolymer surface films have been sometimes observed at the liquid–solid interface and have been connected with the substitution of shorter chains by longer macromolecules in the surface layer (30). Although this process can result in a subtle decrease in the system free energy, it cannot lead to noticeable changes in the surface tension. Indeed the surface tension is determined first of all by the monomer concentration in the proximal region (31) and cannot depend significantly on the length of the adsorbed macromolecules. Stronger effects could be expected if the macromolecules had some small parts of higher hydrophobicity. In this case the slow decrease in the surface tension could be explained by conformational transitions in the surface layer accompanied by the increase in adsorption of more hydrophobic segments. The latter process can lead to formation of a quasibrush structure at high concentrations. However, this mechanism is more probable for block copolymer solutions and is hardly possible for the system under investigation.
DYNAMIC SURFACE PROPERTIES OF POLY(VINYLPYRROLIDONE) SOLUTIONS
Kim and Cao assumed that the change in solvent quality in the surface layer of relatively concentrated aqueous PEO solutions could lead to surface aggregation and to additional reduction of the surface tension (32). However, to the best of our knowledge there are no data indicating similar changes of the solvent quality for PVP solutions. Besides, slow time effects have not been discovered for PEO solutions, thus indicating the significant difference between these two systems. It is more probable that anomalous behavior of surface properties at high PVP concentrations is caused by traces of impurities of high surface activity. It is well known that their influence can be overwhelming in studies of adsorption kinetics (6, 33–36). Enormous efforts have been directed to elucidate the role of impurities and to minimize their effects. To the best of our knowledge the polymer adsorption films have not been investigated yet in this respect. Figure 1 shows that the equilibrium surface pressure of PVP is rather low (about 3 mN/m) in a broad concentration range. This means that if the surface activity of a substance is high, even small traces can be sufficient in order to exceed the PVP surface pressure. In this case the impurity will displace the polymer from the surface layer. The displacement of polymers including proteins by conventional surfactants has been extensively studied for the last few years (37–40). Note that the chemical nature of the admixture is not known in our case. This can be, for example, a scarcely soluble surfactant or a polymer. It is only important that its concentration is extremely low and the surface activity is high. At low and moderate PVP concentrations the total admixture concentration is insufficient to create a surface pressure that exceeds 3 mN/m. While the PVP surface pressure is almost independent of concentration (Fig. 1), the impurity equilibrium surface pressure can increase with concentration and at about c > 0.1 wt% for PVP10 and at c > 0.5 wt% for PVP55 exceeds this threshold. Then PVP is gradually displaced from the surface by the slowly adsorbing impurity (Fig. 2). At small admixture concentrations, its adsorption rate can be extremely slow (33–36). To check out the proposed mechanism of slow processes observed at high PVP concentrations and to elucidate the role of impurities we used the method of Lunkenheimer and Miller and subjected the adsorbed surface film to expansion and subsequent contraction in the Langmuir trough during the equilibration (34). If this procedure was carried out within a few minutes after the formation of the fresh interface, the amplitude of the surface tension change was relatively low and the final value was close to the surface tension before the contraction. However, if the surface contraction and expansion were repeated in a few hours when one can expect the accumulation of the impurity in the surface layer, the amplitude was significantly larger and the final surface tension value exceeded significantly the value before the contraction. The latter results are typical for systems containing a slowly adsorbing (desorbing) impurity (33, 34) and were not observed at lower PVP concentrations where the influence of impurities was significantly weaker. Indeed the contraction is followed by impurity desorption, which leads to large losses of the impurity in the surface layer. The
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FIG. 4. Concentration dependence of εr (solid symbols) and εi (open symbols) of PVP10 and PVP55 (crosses) solutions at frequencies of 0.05 Hz (squares), 0.5 Hz (triangles, crosses), and 270 Hz (circles).
subsequent expansion does not compensate for this loss because of the slow admixture adsorption, and the surface tension does not return to the value preceding contraction. Note that it is hardly possible to explain all the observed time effects if one assumes only the possibility of conformational transitions in the surface layer without any influence of the admixture desorption– adsorption. Our data on the dynamic surface elasticity of PVP solutions (Fig. 4) also confirm this interpretation. At c < 0.1 wt% for PVP10 and at c < 0.2 wt% for PVP55 both components of the surface elasticity are typical for solutions of nonionic polymers (16, 17) and do not exceed 6 mN/m, while at higher concentrations the surface elasticity increases by several times and becomes comparable with values for solutions of conventional surfactants (1, 7, 23). The problem of the admixture chemical nature in PVP solutions is beyond the scope of this work. Even for solutions of conventional surfactants this chemical problem would be difficult to solve. For polymer systems it can be significantly more complicated. Thus only the results of this work at low and medium concentrations (c < 0.1 wt% for PVP10 and at c < 0.2 wt% for PVP55) correspond more or less to a pure PVP adsorption film. At higher concentrations an admixture probably determines the surface properties. The admixture concentration for PVP10 is probably higher than that for PVP55, which leads to the more extended range of the constant surface properties for solutions of the latter polymer. To study this problem further we measured the dynamic surface elasticity. The dynamic surface elasticity ε in the frequency range from 0.007 Hz up to 0.11 Hz was determined by the oscillating barrier method. The sinusoidal oscillations of the area A of the liquid surface in the Langmuir trough generate oscillations of the surface tension measured by the Wilhelmy plate. Both periodical functions of time γ (t) = γ (0) + δγ (t) and A(t) = A(0) + δ A(t) can be represented in the complex form, and the complex surface
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NOSKOV, AKENTIEV, AND MILLER
elasticity at the given angular frequency can be determined as a ratio, ε(ω) = δγ /δ ln A.
[6]
At higher frequencies the dynamic surface elasticity was calculated from the measured characteristics of longitudinal surface waves (in the frequency range from 0.2 Hz up to 3 Hz) or transverse capillary waves (at higher frequencies up to 520 Hz). The dependence of the length of transverse surface waves on concentration is determined by the surface tension and as a result the corresponding dependence for PVP solutions resembles the curve in Fig. 1. The concentration dependence of the damping coefficient α is mainly determined by the surface elasticity and turns out to be more complicated. Figure 5 shows as an example the dependence α(c) for solutions of PVP10 at a frequency of 200 Hz. Similar curves were obtained for other frequencies and for PVP55 solutions too. The results in Fig. 5 are typical for polymer solutions and differ from the α(c) dependences for conventional surfactants by significantly slower changes in concentration and by lower values of the damping in the region of the local minimum (16, 17). This indicates lower values of the dynamic surface elasticity and its more gradual change with concentration in the former case. For more careful investigation of the dynamic surface properties both the real εr and the imaginary εi components of the dynamic surface elasticity were calculated from the characteristics of transverse and longitudinal surface waves according to the dispersion relation (17) ε˜ = ε˜ r + ε˜ i =
ρω2 [ρω2 − (σ k 3 +ρgk) tanh(kh)] + 4iρµω3 k 2 + 4µ2 ω2 k 3 [m tanh(kh) − k] , mk 2 [ρω2 − (σ k 3 + ρgk) tanh(kh)] + k 3 (σ k 3 +ρgk)
[7]
FIG. 6. Frequency dependence of εr (solid symbols) and εi (open symbols) of PVP10 solutions at concentrations 0.004 wt% (squares) and 0.000105 wt% (triangles).
wavelength, m 2 = k 2 − iωρ/µ, Re[m] > 0, ρ is the density of the subphase, µ is the shear viscosity of the subphase, g is the gravitational acceleration, and h is the depth of the liquid (in our setup h equals 15 mm). Figures 6 and 7 show some examples of the frequency dependence of both components of the surface viscoelasticity for PVP10 and PVP55 solutions at different concentrations. It has been shown recently that the characteristic time of the relaxation process in PEG adsorbed films equals 0.06 s (16, 17). All results for PVP solutions including those in Figs. 6 and 7 give no distinct evidence of any relaxation processes in the frequency range from 0.007 Hz up to 520 Hz. However, this can only be a consequence of the low dynamic surface elasticity. Indeed in the concentration range from 0.0001 wt% up to 0.1 wt% the real
where k = 2π/λ + iα is the complex wave number, λ is the
FIG. 5. Concentration dependence of the damping coefficient of transverse capillary waves for PVP10 solutions.
FIG. 7. Frequency dependence of εr (solid symbols) and εi (open symbols) of PVP55 solutions at concentrations 0.00003 wt% (triangles) and 0.01 wt% (squares).
DYNAMIC SURFACE PROPERTIES OF POLY(VINYLPYRROLIDONE) SOLUTIONS
part of the elasticity changed only from 1 mN/m up to 5 mN/m and the imaginary part from 0 up to 2 mN/m, and only in the limiting cases at low and high concentrations were these values exceeded. Thus any frequency changes in the elasticity could lie within the error limits, which are about ±0.5 and ±1 mN/m for εr and εi , respectively, in the medium concentration range. Figure 4 shows the concentration dependence of the dynamic surface elasticity for solutions of PVP10 and PVP55 for different frequencies. One can see again that the surface elasticity is almost independent of frequency but the concentration dependence of the real component at least is distinct enough. The abrupt increase in the elasticity at high concentrations (c > 0.1 wt% for PVP10 and at c > 0.2 wt% for PVP55) can be a consequence of the displacement of PVP from the surface layer by a stronger surface-active admixture. High values of the elasticity in this concentration range can indicate the nonpolymeric nature of the impurity. Although no equilibrium adsorption films were obtained in this concentration range, the measured values of εr and εi are probably close to the equilibrium because the surface elasticities do not change in the error limits during the final steps of the equilibration. At lower concentrations PVP chains in the surface layer determine the surface viscoelastic properties. One can see that εr gradually decreases from about 5 mN/m to about 1 mN/m for both polymers when the concentration increases up to 0.01 wt%. This decrease in the elasticity was obtained for PEG and PEO solutions too and is probably typical for solutions of nonionic linear flexible polymers (16, 17). At concentrations lower than about 3 × 10−5 wt% the equilibration process requires too much time and only the elasticity of the system far from equilibrium can be measured. One can assume that the elasticity goes through a maximum when the PVP concentration is changed from zero to 3 × 10−5 wt%. Measuring the time dependence of the surface elasticity can check this conclusion. Indeed a gradual increase in the PVP adsorption will lead to changes in the surface concentration from zero to the equilibrium value. A maximum of the real component of surface elasticity can be indeed observed in Fig. 8 where both components are plotted as a function of time for c = 3 × 10−5 wt%. The maximum of εr is about 6 mN/m, which obviously must correspond to an equilibrium bulk concentration much lower than 3 × 10−5 wt%. The decrease in the dynamic surface elasticity with increasing concentration at a given frequency of perturbations is also sometimes observed for solutions of conventional surfactants of low molecular weight (23, 24). However, in that case the rate of the decrease is significantly higher, which can be easily explained by the fast decrease in the diffusion relaxation time for surfactants with increasing concentration. When this characteristic time approaches the period of perturbations the dynamic surface elasticity begins to drop. Figure 4 shows that this explanation cannot be used for polymer solutions, where the decrease of εr is significantly slower and does not depend on the frequency in the broad frequency range from 0.007 Hz up to 520 Hz. For most of the frequencies and concentrations under investigation
423
FIG. 8. Kinetic dependence of εr (solid symbols) and εi (open symbols) of PVP55 solutions at concentration 0.00003 wt%.
the period of perturbations exceeds the characteristic diffusion time. The similarity between the surface viscoelastic properties of PVP solutions and PEG and PEO solutions allows us to use the dynamic model (17, 19), as outlined above, also for PVP. At low concentrations the PVP chains are unfolded and lie almost entirely in the proximal region of the surface layer without loops and tails protruding into the adjacent bulk phase (pancake conformation). In this case the film is purely elastic at frequencies under investigation and Eq. [4] holds. This concentration range expands approximately up to the region of the elasticity maximum. At higher concentrations the chains cannot unfold in the surface layer during the adsorption process completely, which leads to the formation of loops and tails in the proximal region. The mechanical stresses in the surface layer can be now relaxed at the expense of the monomer exchange between two regions of the surface layer. The monomers are squeezed into the region of loops and tails upon compression or drawn into the proximal region upon expansion. If the period of perturbations is comparable with the corresponding relaxation time the surface film becomes viscoelastic (17–19). The information on the structure of the adsorbed PVP films studied in this work is insufficient for calculations of the dynamic surface elasticity from Eq. [1]. On the other hand, the region of the elasticity maximum corresponds to very low PVP bulk concentrations, which can be investigated only as transient states during the equilibration process (Fig. 8). When we measured the dynamic surface elasticity using small perturbations of the equilibrium state, the obtained values were too low for a determination of the relaxation times (Fig. 4). Here we can use only the similarity between the adsorbed films of PVP and PEG and assume that the relaxation times for PVP are also comparable with the periods of perturbations used in this work, at least at concentrations just above the region of the elasticity maximum. The decrease in the dynamic surface elasticity with concentration can probably give some grounds for this point of view.
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CONCLUSIONS
The results on the dynamic surface tension and dynamic surface elasticity of PVP adsorbed films have shown that an impurity gradually displaces PVP chains from the surface at concentrations higher than 0.1 wt% and thus leads to slow equilibration of the system. Only in the range of low and middle concentrations does the adsorption of PVP chains determine the surface properties. At concentrations lower than 0.1 wt% the dynamic surface elasticity gradually decreases when PVP is added to the solution. This behavior is similar to that of solutions of PEO and PEG. Although the relaxation time was not determined for PVP solutions, we consider that the decrease in the elasticity is a consequence of the increase in the number of loops and tails in the distal region of the surface layer. ACKNOWLEDGMENTS This work was financially supported by the Russian Foundation of Fundamental Research (Project RFFI 99-03-32247a). A.V.A. is grateful to INTAS for the fellowship grant for young scientists (YSF 00-166).
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