Potentiometric Titration, Isothermal Titration Calorimetry, and L

J. Phys. Chem. B 2002, 106, 1195-1204

1195

Dissolution Behavior of HASE Polymers in the Presence of Salt: Potentiometric Titration, Isothermal Titration Calorimetry, and Light Scattering Studies C. Wang and K. C. Tam* School of Mechanical and Production EngineeringNanyang Technological UniVersity, 50 Nanyang AVenue, Singapore 639798

R. D. Jenkins The Dow Chemical Company, Asia-Pacific Technical Center, 16 Science Park DriVe, The Pasteur, Singapore 118227 ReceiVed: February 26, 2001; In Final Form: October 19, 2001

Potentiometric titration, static and dynamic light scattering, and isothermal titration calorimetry were used to study the salt effects on the dissolution behavior of Hydrophobically Modified Alkali-Soluble Emulsion (HASE) polymer emulsions in aqueous medium.The negative logarithm dissociation constant (pKa) curves reveal that HASE polymer exhibits a conformational transition from a compact hard sphere to a random coil during the process of neutralization. Addition of a neutral salt reduces the energy necessary to extract protons from carboxylic acid groups, which favors the neutralization process. The latex particles expand with extent of neutralization (R) in the early stage of titration, thereafter the swollen particles dissociate into smaller clusters. The addition of salt screens the electrostatic repulsion between the polymer chains, and consequently reduces the hydrodynamic radius (Rh) of the polymer clusters. The results also show that the polymer chains tend to form intramolecular association rather than intermolecular association in the presence of salt, which promotes the dissociation of polymer particles. The thermodynamic quantification of the dissolution behavior of model HASE polymer was achieved using the isothermal titration calorimetric technique. The results reveal that neutralization is an exothermic process dominated by enthalpy. The comparison of the titration data in different salt conditions show that the ∆G for the neutralization process is more negative at high salt content, suggesting that the dissolution is enhanced by the presence of a neutral salt.

Introduction Water-soluble associative polymers consisting of a hydrophilic backbone with hydrophobic groups distributed at the ends or along the polymer backbones, are widely used as thickeners in paint formulations and paper coatings. When the polymer dissolves in water, clusters of hydrophobic domains are formed yielding a network structure. Such structure induces a large increase in the solution viscosity, producing a viscoelastic gellike fluid. HASE (Hydrophobically Modified Alkali-Soluble Emulsion) polymers are long-chain acrylic polymers, typically copolymers of ethyl acrylate and methacrylic acid, containing hydrophobic pendant side groups. One of the distinguishing features of these polymer structures is that the hydrophobic substituents are separated from the polymer backbone by a polyethylene-oxide (PEO) spacer chain. An increase in the pH causes the ionization of acid groups, leading to the solublization of latex particles, which give rise to interesting changes in the polymer conformation.1-3 The dispersions at low pH possess a water-like viscosity. Raising the pH of a moderately concentrated polymer solution to higher than 7, produces a large increase in the solution viscosity.4-7 A number of studies have focused on developing an understanding on the dissolution behavior and conformational transi* To whom correspondence should be addressed. Fax: 65-791-1859. E-mail: [email protected].

tion of polyelectrolyte systems, such as poly(acrylic acid) (PAA), poly(methacrylic acid) (PMAA), and poly(methacrylic acid-comethylenebisacryamide) microsphere (PMAA microgel) using a number of different experimental techniques, e.g. potentiometry, X-ray scattering, viscometry and electrophoretic mobility measurement.8-13 The detailed and direct information on the conformational transition can be obtained from the analysis of negative logarithm dissociation constant (pKa) versus neutralization degree (R) curve. For low molar-mass weak acid, pKa increases very slightly over a wide range of R values and remains closed to pK0 (the value of pKa at zero neutralization degree). In the case of PAA, the values of pKa increase proportionately with R. In the case of PMAA, the plot of pKa against R shows a maximum and a minimum. The nonmonotonic dependence of pKa on R is attributed to the discontinuous conformational transition during the process of neutralization of PMAA.8 This transition is attributed to the change from a compact, polysoap-like conformation to an expanded, polyelectrolyte-like coil conformation (globule to coil).9,10 A swelling transition is also found in PMAA microgels, where the microgel volume increases from 13.0 to 96.4 µm3 as the pH increases from 2.0 to 7.8, and the extent of swelling is a dependent on the cross-linking density, functional groups grafted on the microgel and ionic strength.11-13 The addition of a neutral salt significantly alters the behavior of HASE particles in aqueous solution. It is known that strong electrostatic repulsions resulting from large amounts of charged

10.1021/jp0107309 CCC: $22.00 © 2002 American Chemical Society Published on Web 01/22/2002

1196 J. Phys. Chem. B, Vol. 106, No. 6, 2002 groups on the polyion are suppressed by the accumulation of small ions from the salt.14-17 Linear flexible polyions are greatly extended by the electrostatic interaction but they contract in the presence of salt to yield a conformation similar to that of uncharged polymers. Addition of salt changes the electrostatic interaction between the macroions, counterions, and solvent molecules. In the titration of weak polyacids or polybases, the relationship between pH and the amount of titrant is different from that in low molecular acids and bases, resulting from strong Coulombic potential around the polyions. The addition of low molecular salts minimizes the difference between the pH curves of polyacids or polybases and low molecular acids and bases.8 Analysis of such titration experiments provides direct information on the effect of salts on the electrical potential surrounding the polyions. The main objective of this paper is to investigate the effects of salt on the dissolution behavior of HASE polymers. It is hoped that such studies will provide a molecular-level understanding on the dissolution and association mechanism of HASE polymers in different salt environments. The experimental techniques used in this study are potentiometric and conductometric titrations, isothermal titration calorimetry (ITC), and laser light scattering (LLS). Information on the conformational transition of various polymeric systems during the process of neutralization can be extracted from careful analysis of potentiometric and conductometric titration results. The dissociation constant (pKa), the intrinsic dissociation constant (pK0), and the Gibbs energy (∆G) can be obtained by analyzing the titration data. Microcalorimetry is a sensitive technique commonly used to determine thermodynamic parameters such as the enthalpy, entropy, Gibbs energy, and equilibrium constant of reaction between HASE polymer and the base. The thermodynamic data provide important information on the interactions between the polymer and base. Laser light scattering (LLS) examines the transport properties of polymer chains in solution. The hydrodynamic radius (Rh) and the radius of gyration (Rg) can be measured by dynamic and static light scattering, respectively. The particle size of polymer cluster in solutions during neutralization and the conformation behavior of these clusters can be elucidated. Experimental Section Materials. The model HASE polymers (HASE-series) examined in this study were synthesized by Dow Chemicals (formerly Union Carbide) at a concentration of 10 volume percent. The chemical structure of these HASE polymers is schematically shown in Figure 1. They have an average molecular weight of approximately 200,000 to 250,000 Daltons determined by static light scattering measurements.18,19 The copolymer was prepared by conventional semi-continuous emulsion polymerization of methacrylic acid (MAA), ethyl acrylate (EA), and associative macromonomer (AM) with the composition of the MAA:EA:AM kept at 49:50:1 percentage moles. The structure of the associative macromonomer used in this study consists of a poly(oxyethylene) chain connected to an alkyl hydrophobic group (RdCnH2n+1) at one end and a vinyl polymerizable group at the other end. The associative macromonomer was prepared by first ethoxylating a linear alkyl primary alcohol with ca. p moles of ethylene-oxide (EO) to make a surfactant, and subsequently reacting the resulting terminal primary hydroxyl group of the ethoxylate part of the surfactant with an unsaturated isocyanate. This connects the ethoxylated portion of the surfactant to a vinyl polymerizable double bond through a urethane linkage. The polymers are designated as

Wang et al.

Figure 1. Chemical structure of HASE polymers.

HASE-p-n, where p is the number of moles of ethoxylation and n is the number of carbon atoms in each hydrophobe. Potentiometric Titration. All potentiometric titrations were conducted using ABU93 Tri-buret Titration System. The electrodes are Radiometer pHG201 pH glass and Radiometer REF201 reference electrodes. All the titrations were performed at 25 °C, in a titration vessel filled with 100 mL of 0.1 wt % HASE polymer solution, and with constant stirring. A 1 M standard NaOH solution (from Merck) was used as titrant. Forty seconds of lag time was allowed between two dosages to ensure that the reaction had reached equilibrium. After each dosage, 200 µL of HASE polymer solution was removed from the titration vessel to a test tube for light scattering measurements. The pH and reference probes are not affected by the macromolecules as the pH probe yields identical pH prior to and after the titration experiments. Isothermal Titration Calorimetry (ITC). The calorimetric data were acquired using a Microcal isothermal titration calorimeter (ITC). This power compensation, differential instrument was previously described in details by Wiseman et al.20,21 It has a reference and a sample cell of approximately 1.35 mL and the cells are both insulated by an adiabatic shield. The titration was carried out at 25.0 ( 0.02 °C, by injecting approximately 5 mM base solution from a 250 µL injection syringe into the sample cell filled with 0.01 wt % polymer solution. The syringe is tailored-made such that the tip acts as a blade-type stirrer to ensure an optimum mixing efficiency at 400 rpm. An injection schedule was automatically carried out using interactive software after setting up the number of injections, volume of each injection, and time between each injection. Dynamic and Static Light Scattering. In this study, the Brookhaven laser light scattering system was used. The equipment consists of a BI200SM goniometer, BI-9000AT digital correlator, and other supporting data acquisition and analysis software and accessories. A 200 mW argon-ion, vertically polarized 488-nm laser was used as the light source. The concentration of HASE polymer solutions used in the light scattering experiments is 0.02 wt %. The G2(t) functions obtained from DLS were analyzed using the Inverse Laplace Transformation technique (REPES for our case) to produce the distribution function of decay time. Several measurements were carried out at 90° for a given sample to obtain an average hydrodynamic radius and the variation in the Rh values is small.

HASE Polymers in the Presence of Salt

J. Phys. Chem. B, Vol. 106, No. 6, 2002 1197

Figure 2. Potentiometric titration behaviors of HASE35-12: (0) in 10-4 M NaCl solution; (]) in 0.01 M NaCl solution; (4) in 0.03 M NaCl solution; (O) in 0.06 NaCl solution; (b) in 0.1 M NaCl solution; (2) in 0.15 M NaCl solution.

Figure 3. The values of pKapp versus neutralization degree for HASE35-12 in aqueous solutions: (0) in 10-4 M NaCl solution; (]) in 0.01 M NaCl solution; (4) in 0.03 M NaCl solution; (O) in 0.06 NaCl solution; (b) in 0.1 M NaCl solution; (2) in 0.15 M NaCl solution.

Results and Discussion

(indicated by the arrows) can be detected from the pH curves. The first equivalence point observed at R ∼ 0.1, characterizing the strong acid-base reaction, caused by the neutralization of a small amount of sulfate (∼SO3H) groups introduced from the initiator during the polymer synthesis.2,27 The second equivalence point at R ) 1 characterizes the complete neutralization of carboxylic groups on the polymer chains. As shown in Figure 2, the pH decreases with the increase of NaCl concentrations before the complete neutralization point. However, the pH values after complete neutralization point (R > 1) are independent of salt concentrations. The addition of salt to polyacid solution screens the electrostatic interaction between the neutralized (ionized) acidic groups, and consequently changes the pH value.8,28-30 In aqueous solution, the polyacid molecule dissociates into a ∼RCOO- anion and a proton, i.e. ∼COOH h COO- + H+. When NaCl is added into the polyacid solution, the sodium ions form an ionic atmosphere in the vicinity of the negatively charged carboxylate groups, which shields the Coulombic interactions between the carboxylate groups and weakens the correlations between them. On the other hand, the negative charges along the polymer chains are stabilized by sodium ions, which favors the dissociation and this shifts the equilibrium to the right-hand side. Therefore the acidic property of the polyacid is enhanced and the pH value is reduced. For R > 1, all the carboxylic groups are neutralized (i.e. dissociated and ionized) and the equilibrium is reached, therefore the pH values are not affected by the salt concentration. The thermodynamic derivation for a partially neutralized polyacid also shows that the pH is dependent on the amounts of salt, which is discussed in Appendix A. Figure 3 shows the comparison of the pKa curves in different salt concentrations. The pKa curves show a similar trend for the polymer in different salt concentrations. The values of pKa increase with R and reach a maximum at R ) ∼0.1. Thereafter, they decrease to a minimum at R ) ∼0.45 and subsequently increase again. The whole process of neutralization can be classified into three stages by the two inflection points indicated by arrows in Figure 3. It is well-known that some polyacids (e.g. poly(methacrylic acid), poly(glutamic acid), and alternating copolymer of maleic acid and hydrophobic monomers) exhibit a conformational transition from a compact globular coil to an expanded hydrated coil, which is described by similar pKa curves as shown in Figure 3.9,10,23-26 Based on this, we can deduce that HASE polymer exhibits similar conformational transition

Potentiometric and Conductometric Titration. The degree of neutralization, R, of the carboxyl group is defined by the equation

R)

[BASE] + [H+] - [OH-] CCOOH

(1)

where [BASE], [H+], and [OH-] are the molarities of added base, free hydrogen ion, and hydroxide ion, respectively, and CCOOH is the total concentration of methacrylic acid groups expressed in moles per liter. The hydrogen and hydroxide ion concentration terms are calculated from the pH, where the activity coefficient is assumed to be unity. With this definition, R ) 1 at complete neutralization. The potentiometric titration of the polyelectrolyte solutions is usually treated in terms of the negative logarithm of the apparent dissociation constant (pKa), defined by the equation

pKa ) pH + log

1-R R

(2)

where pKa is the sum of two terms:

dGel pKa ) pK0 + 0.434 RTdR

(3)

pK0 is the intrinsic dissociation constant independent of R, R the gas constant, T the absolute temperature, and Gel the electrostatic Gibbs energy term, which corresponds to the energy required to overcome the electrostatic force to extract a proton from a charged polyion.13 The pK0 values were obtained by extrapolating the titration curves to zero neutralization degree (R ) 0), and ∆Gel (from R ) 0 to 1) can be obtained from the graphical integration based on eq 4.

∆Gel ) 2.30RT

∫01 [pK(R) - pK0]dR

(4)

where pK(R) is the dissociation constant at any given R values and pK0 is the intrinsic dissociation constant.23-26 Figure 2 shows the comparison of pH curves obtained from titrating 1 M NaOH into 0.1 wt % HASE35-12 solutions containing different amounts of NaCl (varying from 10-4 M to 0.15 M), where the pH values were plotted as a function of neutralization degree, R. Two distinct equivalence points

1198 J. Phys. Chem. B, Vol. 106, No. 6, 2002

Wang et al.

Figure 4. Dependence of ∆Gel on NaCl concentration in polymer solutions.

TABLE 1: Potentiometric Characterization of HASE Polymer salt concentration (M)

pK0

∆Gel (kJ/mol)

10-4 0.01 0.03 0.06 0.1 0.15

5.64 5.62 5.79 5.84 5.86 5.86

8.68 5.58 3.35 2.12 1.34 0.98

from a compact latex particle to a swollen hydrated coil during neutralization. This conformational change indicated by the negative slope between the two inflection points in the pKa curves is governed by the balance of hydrophobic attraction and electrostatic repulsion forces. This deduction is further confirmed by light scattering data, which will be discussed later. Another striking feature of Figure 3 is that the pKa values decrease significantly with increasing NaCl concentrations. As discussed earlier, the addition of salt favors the dissociation of carboxylic groups, which enhances the dissociation constant Ka, yielding a lower pKa value. By graphical integration of eq 4, which is also known as the extended Henderson-Haselbalch equation, the pK0 and ∆Gel values can be determined. Although the ∆Gel values may include some errors due to the ambiguity of determining the pK0, the magnitude of this parameter is reasonably reliable. The pK0 and ∆Gel values at different salt concentrations are summarized in Table 1 and the values of ∆Gel are plotted as a function of NaCl concentrations in Figure 4. The pK0 values listed in Table 1 are essentially independent of salt concentrations. However, the addition of salts significantly reduces the electrostatic Gibbs energies, ∆Gel. ∆Gel corresponds to the additional work required to overcome the Coulombic attraction between H+ and RCOO- for extracting one mole of protons from the polyacid at a given R. As shown in Figure 4 and Table 1, the ∆Gel decreases rapidly from 8.67 kJ/mol to 2.12 kJ/mol when the NaCl concentration increases from 10-4 M to 0.06 M. Additional NaCl results in the further reduction of ∆Gel, but the curve begins to level off at high salt concentration (0.1 M). When the NaCl concentration reaches ∼0.18-0.2 M, the HASE polymer particles are destabilized and they flocculate due to charged shielding effects, hence titration experiments could not be performed beyond this limit. The results obtained from the potentiometric titration suggest that the Coulombic attraction between H+ and RCOO- is screened by the addition of salt, which significantly reduces the energy required to extract protons from carboxylic groups. Thus, the addition of salt favors the dissociation of HASE polymers. Dynamic and Static Light Scattering. The concentration of the solutions investigated by light scattering measurements

Figure 5. Distribution functions for HASE35-12 in 0.1 M NaCl aqueous solution at different degree of neutralization.

is 0.02 wt %, which is in the dilute solution regime as the overlap concentration, as defined by C* ) 1/[η], is approximately equal to 0.5 wt %. Under such conditions, the behavior of individual particles can be characterized. The relaxation time distribution functions measured at 90 degrees during the neutralization process for HASE35-12 in 0.1 M NaCl solution are given in Figure 5 . The features of the distribution functions obtained in other salt concentrations are identical and are described below. Before titrating NaOH into the polymer solution (R ) 0), the distribution function is described by a narrow range of relaxation times with a large amplitude, which corresponds to the insoluble polymer particles that strongly scatter light. As the NaOH was titrated into the solution, the distribution function broadens, and the relaxation time shifts to a higher value with a reduced amplitude. This corresponds to the swelling of polymer particles driven by the increasing electrostatic repulsion between ionized carboxylate groups. When the pH reaches approximately 5.7, the relaxation time decreases and a second distribution characterizing a smaller particle size appears. The slow mode corresponds to the dissociated small clusters from the swollen coil and the fast mode corresponds to single HASE polymer chains in aqueous solution.18 The apparent hydrodynamic radius (Rhapp) can be obtained from the Stokes-Einstein equation:

Rh )

kTq2 6πηΓ

(5)

where k is the Boltzmann constant, q is the scattering vector (q ) 4πn sin(θ/2)/λ, where n is the refractive index of the solution, θ is the scattering angle, λ is the wavelength of the incident laser light), η is the solvent viscosity, and Γ is the decay rate.


Figure 6. Rhapp(DLS) versus R in 0.1 M NaCl aqueous solutions: (b,O) HASE35-01; (2,4) HASE35-04; (9,0) HASE35-12; ([,]) HASE35-16. (Filled symbols for larger polymer clusters and open symbols for single polymer chains).

Figure 7. 1/I sin θ versus sin2(θ/2) for HASE35-12 in 0.1 M NaCl aqueous solution at different degree of neutralization.

Figure 6 shows the Rh values plotted against R for HASE35 series polymers in 0.1 M NaCl solutions, where the close symbols represent the particle size of polymer cluster and the open symbols represent single polymer chains. The Rh value of insoluble polymer particle is approximately 55 nm before neutralization. With the addition of NaOH, the HASE polymer particles swell and reach a maximum Rhapp of approximately 80 nm at R ∼ 0.25. With further addition of NaOH, the swollen particles dissociate into smaller clusters because of the overwhelming electrostatic repulsive forces between the carboxylate groups. Therefore, Rh decreases and reaches the minimum value of approximately 45 nm at R ∼ 0.4. Beyond this, a second smaller particle size, corresponding to single polymer chain is detected. Both particle sizes (cluster and single polymer chain) are independent of the degree of neutralization, where the Rhapp of the single polymer chain and cluster remain constant at ∼15 and 50 nm, respectively. Figure 7 shows a graph of (1/I′ sin θ) plotted against sin2(θ/2) for HASE35-12 at two different degrees of neutral-


Figure 8. Rgapp(SLS) versus R in 0.1 M NaCl aqueous solutions: (b) HASE35-01; (2) HASE35-04; (9) HASE35-12; ([)HASE35-16.

ization. I′ is the scattering intensity determined by the photon detector for measurement angles θ ranging from 45 to 120 degrees. It is evident that the static light scattering experimental data can be fitted by straight lines for all the samples. The radius of gyration (Rg) was obtained from the slope of (1/I′ sin θ) versus sin2(θ/2), where the values of Rg were directly computed using the Brookhaven static light scattering software. The Rg values of 0.02 wt % HASE35 series polymers in 0.1 M NaCl aqueous solutions are plotted against R in Figure 8 . Comparison of the Rh and Rg curves plotted in Figures 6 and 8 shows that they exhibit a similar trend in the course of neutralization. The Rg values remained essentially constant at Rg ∼ 80 nm when R exceeds ∼0.6. Before neutralization, the HASE polymer exists as insoluble latex particles, where the polymer chains associate with each other to form compact hard spheres. When NaOH is titrated into the latex dispersion, the carboxylic acid groups on the surface of the particles are neutralized and ionized to carboxylate groups. This causes the polymer particles to swell, which significantly increases the diameter of the particle. As shown in Figures 6 and 8 respectively, the hydrodynamic radius and the radius of gyration increase sharply, reaching a maximum size at R equals to 0.25. However, with further addition of NaOH, both Rh and Rg decrease owing to the dissociation of swollen polymer particles into several smaller clusters. After passing through the minimum value, a slight increase in Rh and Rg is observed owing to the process of swelling of dissociated polymer clusters. The process of swelling and dissociation is completed at R equal to 0.6, thereafter, both Rh and Rg remained unchanged. The parameter F (Rg/Rh) is introduced to examine the conformation of the polymer particles during the process of neutralization. In the present study, Rg corresponds to the particle size of the large cluster, since the scattering intensity of the large cluster is much stronger than that of single polymer chains. Figure 9 shows the dependence of F on R. F equals approximately 0.75 before neutralization, which agrees with the theoretical value of F for a hard sphere with a well-distributed density of 0.774. It then increases with R and reaches a maximum value ranging from 1.5 to 1.7 at R equal to 0.6. Thereafter, it remains essentially constant and fluctuates at around 1.5, which is very close to the theoretical F value (1.502) for Gaussian chain in a good solvent. The addition of salts suppresses the electrostatic interactions between the charged groups of HASE polymers, which also considerably alters the light scattering behavior of the polymer solution. Figure 10 shows the comparison of dynamic light scattering behavior of HASE35-12 solution in different salt


Wang et al.

Figure 9. F(Rg/Rh) versus R within 0.1 M NaCl aqueous solutions: (b) HASE35-01; (2) HASE35-04; (9) HASE35-12; ([) HASE3516.

Figure 11. The dissolution mechanism of HASE polymers in different salt conditions. Figure 10. Rhapp versus R for HASE35-12: (0) in 10-4 M NaCl solution; (]) in 0.01 M NaCl solution; (4) in 0.03 M NaCl solution; (b) in 0.1 M NaCl solution.

concentrations. As shown in Figures 10, HASE polymer exhibits a swelling-dissociation behavior during the process of neutralization in all salt conditions examined in this study. However, the extent of swelling, the R value corresponding to the maximum Rh, and the particle size when the polymer is completely neutralized are different depending on the amounts of NaCl present in the solution. In 10-4 M NaCl solution, the particles swell and reach the maximum Rh value of approximately 200 nm at R ) 0.4. Thereafter, Rh decreases with R and reaches a minimum value of approximately 80 nm at R ) 0.7, where it remains unchanged. With increasing NaCl concentrations, the R value corresponding to the maximum Rh decreases from 0.4 in 10-4 M NaCl to 0.25 in 0.1 M NaCl. Moreover, the maximum Rh value also decreases from ∼200 nm to ∼80 nm when the NaCl concentration increases from 10-4 M to 0.1 M. The differences in the magnitudes of Rh and the R value corresponding to the maximum Rh in different salt conditions may be correlated to the diverse conformations at various salt conditions. During the process of swelling, the stiffness of polymer chains caused by the strong electrostatic repulsion of charged carboxylate groups permits the formation of intermolecular hydrophobic junctions. Therefore, the structure of the swollen particle is relatively loose and open, as indicated by the high Rh value shown in Figure 10. The addition of salt suppresses the electrostatic repulsion of carboxylate groups and increases the flexibility of HASE polymer backbones, which favors the formation of intramolecular junctions. Hence the structure of swollen particles becomes more compact, yielding

a lower Rh. From Figure 10, it can be deduced that the shrinkage of the polymer backbones allows the dissociation of swollen particles into smaller individual clusters at a lower R. The dissolution mechanism of HASE polymer in the presence and absence of salt is depicted in Figure 11. Isothermal Titration Calorimetry (ITC). Figure 12a shows the thermogram that depicts the raw heat signal (cell feedback -CFB) after subtracting the baseline, neglecting the heat of dilution of the titrant (which is only significant when titrant concentration is high) from the gradual injections of 5 mM NaOH solutions into 0.01 wt % HASE35-12 solution. Integration of the area under the raw signal curve at each injection normalized to the degree of neutralization, R′, yields the differential enthalpy curves as shown in Figure 12b. The apparent degree of neutralization, R′, has the same physical meaning as R defined by eq 1, whereas the correction for free hydrogen and hydroxide ions is neglected. With this definition, the complete neutralization point should be reached at R′ ∼ 1. The features of the thermogram and enthalpy curve shown in Figure 12 generally represent the swelling behavior of HASE polymers. As discussed earlier, HASE polymer exist as insoluble latex particles before neutralization, where most of the carboxylic groups are buried inside the particles and are not accessible. Thus, the enthalpy corresponding to neutralization is fairly low (approximately -3 kcal/mol) at the early stage of neutralization. With further addition of NaOH, more polymer chains are ionized and the particles swell, which favors the penetration of OH- groups into the particles and neutralize the carboxylic groups inside the particles. Therefore, the enthalpy becomes more pronounced with increasing R′, where it reaches



Figure 12. Calorimetric titration of 5 mM NaOH into 0.01 wt % HASE35-12 solution at 25 °C. (a) Thermogram showing Cell Feedback (CFB) versus time. (b) Differential enthalpic curves versus degree of neutralization and fit line to a model involving two sets of binding sites.

a maximum value of approximately -13 kcal/mol at R′ ) 0.25 and then levels off (Figure 12b). The plateau over the R′ range, from 0.25 to 0.5, corresponds to the neutralization of swollen particles, which is identical to the results of the potentiometric titration and dynamic light scattering measurement. The acids present in the aqueous phase and at the surface of the polymer clusters are neutralized and the radius of latex particles reaches the maximum value over the same range of R′. When R′ reaches approximately 0.6, the enthalpy curve decreases sharply at the equivalence point of R′ ∼ 1, and this corresponds to the complete neutralization of carboxylic groups. The solid line shown in Figure 12b is the nonlinear fitted curve, where the detailed description of the fitting model is given in Appendix B. The theoretical curve fits very closely to the experimental data points. The values of the equilibrium constant K, ∆H, and ∆G obtained from the model fitting, and the average deviations from the mean are compiled in Table 2. The change in the Gibbs energy of a reaction is given by the expression;

∆G ) ∆H - T∆S

(6)

The value of ∆G is controlled by two factors, the enthalpy (∆H), and the entropy (∆S). For an isothermal system, the change in the Gibbs energy is the only criterion for determining

if a reaction can proceed spontaneously, as any spontaneous process decreases the Gibbs energy of the system (∆G < 0). The neutralization of HASE polymer in aqueous solution is exothermic and the change in the enthalpy is ∼56 kJ/mol. Before neutralization, the molecules of HASE polymer are nonpolar and cannot dissolve in polar solvent such as water. With the addition of NaOH, the carboxylic groups are ionized and thus the polarity of polymer molecules is enhanced, which strengthens the polymer-solvent interaction and consequently the polymer becomes soluble. This category of dissolution is normally exothermic because of the interaction between the polymer and solvent molecules. On the other hand, the entropy change is negative (∆S is -145 J/mol K), which indicates that the whole system is more ordered when the polymer dissolves in the water phase. The entropy determined from ITC measurements is not pure mixing entropy; it is the overall entropy caused by several contributing factors. It contains the entropy for polymer/water mixing, dissociation of carboxylic groups along polymer chains, counterion condensation around the carboxylate groups, and hydration of carboxylate groups by the enhanced polymer-solvent interaction. It should be noted that the latter two contributing factors account for the negative entropy. Before neutralization, the system consists of well-dispersed polymer particles and completely dissociated NaOH solution in the form of sodium and hydroxyl ions. When NaOH is titrated into the polymer solution, the protons on the carboxylic acid groups along the polymer chains are neutralized by the hydroxides from the base and are removed from the polyions into the water phase. The counterions (Na+) are condensed around the neutralized carboxylate groups and consequently loose their translational entropy. Furthermore, the polymer particles undergo a swelling from a compact hard sphere to an expanded hydrated coil during neutralization, and the formation of ordered water structure around the carboxylate groups caused by the improved polymersolvent interaction also reduces the entropy of system. Obviously, the whole system is more ordered after neutralization and the entropy change is negative. Hence it can be concluded that the entropy factor is unfavorable for the dissolution to proceed. However, since the absolute value of ∆H is larger than T∆S, ∆G is negative, and therefore the polymer can spontaneously dissolve in water when the base is added and the dissolution is dominated by enthalpy. Figure 13 shows the comparison of the differential enthalpy curves obtained from titrating 5 mM NaOH into 0.01 wt % HASE35-12 in different NaCl solutions. The enthalpy curves show similar trends for all the NaCl concentrations examined. By comparing the curves shown in Figure 13, it is noted that the shape of titration curve is affected considerably by the addition of salt. The enthalpy curve corresponding to the titration of HASE polymer in high NaCl concentrations (i.e. 0.03 M, 0.06 M, and 0.1 M) are essentially flat in the range of R′ from ∼0.2 to ∼0.90, thereafter it increases sharply at the equivalence point, R′ ∼ 1 (marked with “A”), which corresponds to the complete neutralization of carboxylic groups. For the HASE3512 in 10-4 M NaCl, the flat region of enthalpy curve is observed over a narrower range of R′ (from ∼0.15 to ∼0.45), thereafter

TABLE 2: Effect of Salt on the Thermodynamic Parameters for Dissolution of HASE Polymera salt concentration (M) 10-4 0.03 0.06 0.1 a

K 105 (

1.19 × 1.50 × 3.57 × 105 ( 5.42 × 104 4.79 × 105 ( 1.13 × 104 5.35 × 105 ( 5.65 × 104 103

∆H (kJ/mol)

∆S (J/mol K)

∆G (kJ/mol)

-55.6 ( 0.16 -54.2 ( 0.49 -52.3 ( 0.56 -52.1 ( 0.47

-145 -77.8 -65.4 -66.1

-28.9 -31.0 -32.8 -32.4

Values for the equilibrium constant and the heat of neutralization were obtained by nonlinear fitting (using Microcal Origin software).


Wang et al. with a strong base is an exothermic process dominated by enthalpy. The comparison of the titration data in different salt conditions shows that the addition of salt increases the values of ∆G, and hence favors the neutralization of HASE polymer. Acknowledgment. We appreciate the support and enthusiasm of Dr. Dave Bassett in this research collaboration between NTU and Dow Chemicals (formerly Union Carbide). We would also like to acknowledge the financial support provided by the National Science and Technology Board of Singapore and the Ministry of Education. Appendix A. Thermodynamic Derivation for Partially Neutralized Polyacid in the Presence of Salt

Figure 13. The calorimetric titration behaviors of HASE35-12: (0) in 10-4 M NaCl solution; (4) in 0.03 M NaCl solution; (O) in 0.06 NaCl solution; (b) in 0.1 M NaCl solution.

the enthalpy increases gradually and exhibits a less distinct equivalence point. The shape of the curves generally represent the cooperativity of the interaction and this is dependent on the product of the equilibrium constant (K) and the concentration of macromolecules ([Mt]) in the cell. The sensitivity of the shape of the titration curve to K[Mt] allows the equilibrium constant to be derived from the calorimetric titration. When the product of the equilibrium constant and macromolecule concentration (K[Mt]) increases, the shape of the binding curve becomes progressively less sensitive to changes in the values of K. In this study, the concentrations of HASE polymer solutions are similar, hence the shape of titration curves indicate that the equilibrium constant in the presence of salt should be higher and the polymer-NaOH interaction is more cooperative than in the absence of salt. All the thermodynamic parameters derived from curve fitting are shown Table 2. The K values are higher and the ∆G values are more negative for the system with higher NaCl concentrations. The thermodynamic parameters obtained ITC at different salt conditions suggest that the addition of salt enhances the equilibrium constant (K), and correspondingly the ∆G of the neutralization. This is identical to the results from potentiometric titrations, where addition of salt decreases the energy necessary to extract a proton from a uniformly charged polyion and thus favors the neutralization. Conclusion The negative logarithm dissociation constant (pKa) curves obtained from the titration data reveal that HASE polymer exhibits a conformational transition from a compact hard sphere to a random coil during the process of neutralization. The average Gibbs energy, which corresponds to the energies required to extract a proton from a charged polyion, decreases when salts are added into the polymer solutions, which suggests that the addition of neutral salt makes it more favorable for the neutralization to proceed. The light scattering studies show that the cationic atmosphere surrounding the neutralized carboxylic groups screens the electrostatic repulsion between polymer chains and this prevents the carboxylate groups from being hydrated. Hence, the Rh value of the polymer particles decreases from ∼200 nm to ∼80 nm as the NaCl concentration increases from 10-4 M to 0.1 M. Addition of salt favors the formation of intramolecular association between polymer chains and promotes the dissociation of polymer particles at lower R. From the thermodynamic parameters (enthalpy, entropy, and Gibbs energy) obtained from ITC, the neutralization of polyacids

In polyelectrolyte solutions, the thermodynamic components must be chosen and treated with some care. In the case of dilute solution of partially neutralized weak polyacid in the presence of neutral salt, the solution consists of four components; i.e., solvent molecules; unneutralized polyacid molecules; neutralized acid; and added salt molecules. Thermodynamics require that components be defined as electrically neutral entities. For our case, in the HASE polymer solution which is partially neutralized by NaOH, the thermodynamic components comprised of the polyion ∼COO- and its counterions, i.e., Na+. Thus, the chemical potential of polyelectrolyte is theoretically defined as the sum of single-ion chemical potentials of ∼COO- (µa) and counterion (µNa+). The following relations are established to describe the chemical potentials of polyelectrolyte (µp) and salt (µs), respectively.

µp ) µa + ZµNa+

(A1)

µs ) µNa+ + µCl-

(A2)

where Z is the number of charged carboxylate groups on the polymer chain. The degree of neutralization, R, is given by the ratio na/np, where np is the total number of acid groups on the polymer chain. The activity Rs of counterions (Na+) in the HASE polymer solution is given by

Rs ) Ra + R0s ) γpca + γ0scs

(A3)

where Ra is the activity of counterions derived from the neutralized carboxylic groups on polymer chains, R0s is the activity of counterions derived from added salts; ca and cs are molar concentrations of counterions of the alkali and added salts, respectively. γp is the activity coefficient of counterions in the neutralized polyacid solution without salts and γ0s is the activity coefficient of counterions in the pure salt solution in the absence of polyions. These definitions of thermodynamic components satisfy the general thermodynamic requirements, hence the Gibbs energy is linearly dependent on the chemical potentials of all components:

G ) n0µ0 + naµp + nsµs

(A4)

where n0, na, and ns are the total numbers of solvent, neutralized carboxylic groups and added NaCl; and µ0, µp, and µs are the chemical potentials of these components, respectively. The degree of neutralization, R, is given by the ratio na/np where np is the total number of carboxylic groups on the polymer chains. By substitution Equations A1 to A3 into A4, the expression of Gibbs energy can be rewritten as:



G ) n0µ0 + naµa + naZµNa+ + nsµCl- + nsµNa+ ) n0µ0 + naµa + nNa+µNa+ + nCl-µCl- (A5) In our case, the molar concentration of added salt (10 mM ∼ 100 mM) is much higher than carboxylic groups (

Potentiometric Titration, Isothermal Titration Calorimetry, and L

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