Aggregation between Xanthan and Nonyphenyloxypropyl β

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Aggregation between Xanthan and Nonyphenyloxypropyl β-Hydroxyltrimethylammonium Bromide in Aqueous Solution: MesoDyn Simulation and Binding Isotherm Measurement Y. M. Li,† G. Y. Xu,*,† A. M. Chen,‡ S. L. Yuan,† and X. R. Cao† Key Laboratory of Colloid and Interface Chemistry, Shandong UniVersity, Ministry of Education, Jinan 250100, P.R. China, and College of Chemical Engineering and Material Science, Zhejiang UniVersity of Technology, Hangzhou 310014, P.R. China ReceiVed: May 29, 2005; In Final Form: September 16, 2005

The aggregation behavior of nonyphenyloxypropyl β-hydroxyltrimethylammonium bromide (C9phNBr) and xanthan (XC) in aqueous solution was investigated by MesoDyn density functional simulation and binding isotherm measurement. The process of aggregate formation and the aggregate morphology are reported. The formation of aggregates includes three stages and the morphology of XC-C9phNBr aggregates is rodlike or ellipsoidal. The effects of temperature and XC concentration on the aggregation are analyzed. Results indicate that the formation of aggregates is an exothermic process, and their formation becomes more difficult and the formation rate decreases with increasing temperature. The formation of aggregates is also related to XC concentration, and it becomes much more difficult when the concentration of XC is higher than 20 vol %. The simulation results agree with binding isotherms of C9phNBr to XC obtained via the potentiometric titration method, which shows a typical cooperative binding between C9phNBr and XC.

1. Introduction In practical applications, surfactants are often used accompanied by macromolecules. The addition of a macromolecule usually changes the properties of surfactant solutions.1,2 For example, some water-soluble macromolecules have been used as antideposition agents in the detergency, viscosifying agents in cosmetics and enhanced oil recovery,3-6 etc. The aggregation between macromolecule and surfactant takes milliseconds or longer to reach equilibrium. The typical size of their aggregate is from tens to thousands of molecules, even bigger. Although there exists much experimental data about their aggregate structures,7,8 computer simulation based on mathematical models may provide a deeper understanding of their collective behavior and the structures formed at equilibrium, especially for their time development, which are difficult to observe from experiments.9-12 The aggregation between macromolecule and surfactant has been modeled by using a detailed molecular description, such as molecular dynamics (MD) and Monte Carlo simulations.13-15 Mesoscopic dynamic models have been paid more and more attention as they form a bridge between fast molecular kinetics and slow thermodynamic relaxation of macroscale properties.16,17 The topic of mesoscopic dynamic is of considerable importance for understanding many types of industrial complex liquids. Groot adopted a dissipative particle dynamics (DPD) model to investigate the macromolecule-surfactant interactions.18 In our previous papers,19,20 the DPD model was also used to study the interactions between a series of surfactants and polymers, such as the morphologies of their aggregates and the variance of the squared end-to-end distance of the polymer. MesoDyn is another important mesoscopic simulation technique, * Author to whom correspondence should be sent. Phone: +86-53188365436. Fax: +86-531-88564750. E-mail: [email protected]. † Shandong University. ‡ Zhejiang University of Technology.

which is based on dynamic mean field density functional theory. An important advantage of MesoDyn is the time integration of functional Langevin equations. Possible applications of MesoDyn include the simulation of the time evolution of micelle formation, drug delivery, phase behavior of block copolymers, formation of mesoscale structures in high impact polystyrenes and coatings, the solution behavior of specific chemical species, etc.21,22 In contrast to previous approaches aimed at classifying morphologies by means of equilibrium theories, the MesoDyn method recognizes the fact that these patterns are irregular in nature, and hence can only be characterized via the dynamic properties of the systems. From an industrial perspective this approach is much more realistic, since typical processing times are orders of magnitude shorter than the thermodynamic relaxation time, and thus such nonperfect states contribute substantially to the behavior of the final material.23 Another important advantage of this method is that there is no a prior assumption on the phases, and the kinetics of phase formation, which is very difficult to observe experimentally, can be studied. Xanthan (XC) is bacterial polysaccharide produced by the bacteria Xanthomonas campestris, which reveals a negative property in aqueous solution. It functions as a hydrophilic colloid to thicken, suspend, and stabilize water-based systems, resulting in its wide application in food, pharmaceutics, personal care, etc.24 In these applications, surfactants are often accompanied by something else. So it is very important to investigate the mixed system of surfactants and XC. The interactions between polyelectrolytes and oppositely charged surfactants have been studied thoroughly by many researchers.25,26 The rheological properties of XC aqueous solution in the presence of surfactant were also discussed in our previous studies.27 In this work, the MesoDyn method was used to simulate the aggregation between XC and the cationic surfactant nonyphenyloxypropyl β-hydroxyltrimethylammonium bromide (C9phNBr) in aqueous solution, and the results are compared with those of the binding

10.1021/jp0528414 CCC: $30.25 © 2005 American Chemical Society Published on Web 10/26/2005

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isotherms of C9phNBr to XC through the potentiometric titration method, using a surfactant-selective electrode.

Now the model for the nonideal free energy functional is introduced,

2. Simulation Method and Details

Fnid[F] )

2.1. Theory in MesoDyn. The basic idea in the MesoDyn method is the density functional theory. It is based on the idea that the free energy F of an inhomogeneous liquid is a function of the local density function F. From the free energy, all thermodynamic functions can be derived. The model used in the MesoDyn project consists of beads of various types I, J, ... with interactions described by harmonic oscillator potentials for the intramolecular interactions (Gaussian chain) and a mean field potential for all other interactions.28 Each bead is of a certain component type representing covalently bonded groups of atoms such as those given by one or a few structural units of a polymer chain. The dynamics of the system is described by a set of functional Langevin equations. They represent diffusion equations in the component densities, which take account of the noise in the system. On a coarse-grained time scale, F0(r) is defined as a collective concentration field of the type I beads at an instant of time and serves as a reference level. There will be a certain distribution of bead positions, defined as Ψ(R11,...,RnN), where Rγs is the position of bead s from chain γ. Given the distribution Ψ, the collective concentration of the bead s from all chains can be defined by the average of a microscopic density operator: n

FI[Ψ](r) ≡

N

∑ ∑δKISTrΨδ(r - Rγs) r)1 s)1

(2)

On the basis of this set of distribution functions, an intrinsic free-energy functional F[Ψ] can be defined:

F[Ψ] ) Tr(ΨHid + β-1Ψ ln Ψ) + Fnid[F0]

(3)

The first term is the average value of the Hamiltonian for internal Gaussian chain interactions.29,30 The second term in the free-energy functional represents the Gibbs entropy of the distribution -kBTΨ ln Ψ. The third term is the mean-field nonideal contribution. Ψ is independent of the history of the system and is fully characterized by the constraints that it represents the density distribution and minimizes the free-energy function. This constraint on the density fields is realized by means of an external potential UI. The constraint minimization of the free energy functional leads to an optimal distribution, which in turn, and by the oneto-one relation between densities, distributions, and external potential, can be written as:

βF[F] ) n ln Φ + β-1 ln n! -

where IJ(|r - r′|)is a mean-field energetic interaction between beads of type I at r and type J at r′. The mean-field intrinsic chemical potentials can easily be derived by functional differentiation of the free energy: µI(r) ) δF/δFI(r). At equilibrium, µI(r) ) constant, which results in the familiar self-consistent-field equations for the mean-field Gaussian chain model. In general, these equations have many solutions, one of which will be a state of lowest free energy; most states will be metastable. On the basis of these equations, the generalized time-dependent Ginzburg-Landau theory can be set up. The following functional Langevin equations for the diffusive dynamics of the density fields are introduced:

∂FA ) MυB∇FAFB∇[µA - µB] + η ∂t

(6)

∂FB ) MυB∇FAFB∇[µB - µA] + η ∂t

(7)

(1)

where δKIS is the Kronecker function with value 1 when bead s is of type I and 0 otherwise. It is assumed that in the liquid with slow relaxation the interactions do not depend on the momenta. A set of distribution functions Ψ is defined with the constraint F0I (r) ) FI[Ψ](r). All distributions Ψ lead to the same density F0I (r) form an equivalence class Ω of distribution functions:

Ω ) {Ψ(R11,...,RnN)|FI[Ψ](r) ) F0I (r)}

∫∫

1 AA(|r - r'|)FA(r)FA(r′) + 2 AB(|r - r′|)FA(r)FB(r′) + BA(|r - r′|)FB(r)FA(r′) + BB(|r - r′|)FB(r)FB(r′) dr dr′ (5)

∑I ∫UI(r)FI(r) dr + βFnid[F]

(4)

The distribution of the Gaussian noise η satisfies the fluctuation-dissipation theorem:

〈η(r,t)〉 ) 0 〈η(r,t)η(r′,t′)〉 ) -

(8)

2MυB δ(t - t′)∇r × δ(r - r′)FAFB∇r' (9) β

where M is a bead mobility parameter. The kinetic coefficient MυFAFB models a local exchange mechanism. The Langevin equations are constructed for an incompressible system with dynamic constraint:

(FA(r,t) + FB(r,t)) )

1 υB

(10)

where υB is the average bead volume. 2.2. Systems Studied. In the MesoDyn method, the molecules are defined on a coarse-grained level as “Gaussian chains of beads”. Each bead is of a certain component type representing covalently bonded groups of atoms. The chain topology depends on the degree of coarsening of the original system. In this work, we used a simpler possible model that the surfactant C9phNBr molecule is shown by two beads, one hydrophobic tail and one hydrophilic head (see Figure 1). The structure of XC is also given. To determine the segment length of macromolecule, the chain dimension of an atomistic chain and that of a Gaussian chain have to be compared.The XC molecule is a homopolymer and the calculation of its Gaussian chain length is easier than that of the diblock or triblock copolymers. Lam et al. reported “if the end-to-end distance and the monomeric lengths are known, the coarsened chain topology and the bead diameter, a, can in principle be calculated”. 31 So the calculation of a Gaussian

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Li et al. TABLE 1: Interaction Parameters between Various Beads Used in Simulationa p h t w

p

h

t

w

0.5 4.0 0.3

0.5 3.0 0.4

4.0 3.0 5.0

0.3 0.4 5.0 -

a Here p, h, t, and w represent XC, the head of the surfactant, the tail of the surfactant, and water, respectively.

Figure 1. The structural formulas of XC and C9phNBr (the left of vertical line is the surfactant tail and the right is the head).

chain length of homopolymer is derived as follows,

n)

N2l2 2 RL,0

(11)

where N is the degree of polymerization, l is the monomer size, and RL,0 is the end-to-end distance of the atomistic chains. The n value calculated with eq 11 is approximately 100. So 100 beads are adapted to represent the XC molecule. To obtain RL,0 of atomistic chains, the RIS Metropolis Monte Carlo (RMMC) method is employed in the cerius2 software by Accelrys.32 The value of N and l are from refs 33 and 34. All the mesoscale simulations and analyses were done with the MesoDyn module in Cerius2 on the SGI workstation. 2.3. Simulation Parameters. The dimensions of the simulation lattice are 32 × 32 × 32. The bond length is set to 1.1543 to ensure isotropy of all grid-restricted operators.23 To ensure a stable numerical algorithm, as an approximation, all bead diffusion coefficients of types h, t, w, p (h ) the headgroup of surfactant, t ) the tail of surfactant, w ) water, p ) XC) were 1.0 × 10-7cm2‚s-1. The simulation temperature was 298 K, and the time step was 50.0 ns. The noise-scaling parameter was 100, and the compressibility parameter was fixed at 10.0.35,36 Another important parameter is the mean-field interaction energy between the different chemical components, which also captures the hydrophilicity and hydrophobicity of the components. For the interactions between XC and water, parameter values can be determined from experimental vapor pressure data.37 But the other interaction parameters (χ) between p, w, t, and h cannot be estimated by the above method. Consequently, χwt used here was estimated to be 5.0 according to the tail of surfactant being nearly insoluble in water, and χwh was estimated to be 0.4 due to the hydrophilic properties of surfactant headgroup, which was estimated by group contribution methods.38 Generally, when χsp > 0.5 (s represents solvent), the macromolecule is not easily dissolved in the solvent.23 Supposing the t and h part of surfactant as a kind of solvent respectively, according to the solubility of XC in them, interaction parameters χtp and χhp are chosen. The values for the interaction parameters between various beads are given in Table 1. 2.4. Binding Isotherms. A surfactant-selective electrode is especially applicable for quantitatively studying the interaction between surfactant and macromolecule.25,39,40 The binding degree (β) of surfactant to macromolecule can be calculated by using the following expression:

β)

C b Cs - Cf ) Cp Cp

(12)

where Cb is the concentration of surfactant bound, Cf is the concentration of free surfactant monomer, Cp is the concentration of the macromolecule, and Cs is the total concentration of surfactant. Therefore, binding isotherms can be constructed by plotting the binding degree β vs Cf. Cs and Cf can be obtained by using the electromotive force (emf) responses in surfactant solutions in the absence and presence of macromolecule via the potentiometric titration method, using a surfactant-selective electrode. In emf measurements the concentration of the sample solution is changed by the titration of a certain amount of surfactant. The amount of bound surfactant can thus be obtained by comparing the binding curve to the calibration line. The XC used in this study was obtained from Zibo Zhongxuan Biological Product Co. Ltd (PR China). C9phNBr was synthesized in our laboratory and purified twice with the acetone and ethanol mixed solvent. All solutions were prepared with Milli-Q water. And the test solution was stirred with a magnetic stirrer during measurements. The titration setup is ZDJ-4A potentiometer (Leici instrument company, Shanghai, China). The surfactant-selective membrane consists of poly(vinyl chloride) (PVC, the weight fraction is 40%) and polymer plasticizer (Elvaloy 742 Du Pont, 60%). 3. Results and Discussion 3.1. Process of Aggregate Formation. In this part, a series of simulations was carried out for the same XC concentration (10 vol %, volume concentration) but different C9phNBr concentrations, which were 5, 10, 20, and 30 vol %, respectively. The isosurfaces of XC for four different systems after 1000 simulation steps at 298 K are presented in Figure 2. This isosurface is a surface formed by points whose density values are identical. In Mesodyn simulation, the phase separation indeed leads to the rapid development of irregular ordered states. Here the isosurface representation figures are used to depict the mesoscopic structure of mixed solutions. It will be seen from Figure 2 that the isosurfaces of XC isodensity (system A and B) are homogeneous, indicating that the XC/C9phNBr aggregate does not form at lower C9phNBr concentration, and with the increasing of C9phNBr, aggregates are formed (system C and D). Their isosurface figures give the morphologies. At 20 vol % C9phNBr concentration, the isosurface of XC is discrete, indicating that the quantity of C9phNBr molecules aggregated on the XC chain is small. With C9phNBr increasing (30 vol %), larger aggregates are formed and more C9phNBr molecules aggregate on the XC chain. The above results also can be confirmed by the time evolution of the order parameter P of each system (Figure 3). Here the order parameter is defined by the mean-squared deviation from homogeneity in the system, which captures the effects of phase separation. The separation of P between different beads indicates that phase separation occurs; it also means that in the system the aggregation between XC and C9phNBr occurs. It will also be seen from Figure 3 that the XC/C9phNBr aggregates do not form at 10 vol % C9phNBr; but as the

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Figure 2. XC isosurface representations after 1000 simulation steps (the volume concentration of the C9phNBr system from A to D is 5%, 10%, 20%, and 30%, respectively). Purple represents lower density of XC bead, gray higher density.

Figure 3. The time evolution of the order parameter P of B, C, and D systems in Figure 2.

concentration of C9phNBr is increased, aggregates form (C, D system). To gain insight into the process of aggregate formation, system C is carefully analyzed. The time evolution of system C indicates that the process of aggregate formation can be divided into three stages. In the first stage, the order parameter of XC remains invariable, indicating that C9phNBr molecules do not start to aggregate on the XC chain. In this stage, the morphology of the system almost does not change and this stage lasts 3 µs. In the second stage, the aggregates form and the

order parameter increases rapidly. It means that once a few C9phNBr molecules aggregate on the XC chain, other C9phNBr molecules aggregate around XC quickly and then the XC/C9phNBr aggregates form. This phenomenon is consisted with the cooperative binding usually observed for the macromolecule/ surfactant system in experiments.40,41 The last stage is the equilibrium stage, although the order parameter fluctuates according to the time step. The fluctuation of the order parameter indicates that the final state of aggregates is in a dynamic equilibrium. It may be found that these two systems go through a similar process by comparing the order parameters of systems C and D. However, it is noticeable that the time necessary for aggregates to start to form in system D is longer than that in system C. This implies that at higher C9phNBr concentration it will take a longer time for their aggregation on the XC chain. But this kind of effect is weaker. The higher the concentration of C9phNBr, the slower the rate of forming aggregates. 3.2. Effect of Temperature. To probe the influence of temperature on the aggregation of XC and C9phNBr, system C (10 vol % XC, 20 vol % C9phNBr) was also simulated at 310 and 323 K (see Figure 3C at 298 K). Figure 4 shows the dimensionless order parameters of system C at different temperatures. Figure 4 indicates that temperature influences the rate of aggregate formation strongly. With increasing temperature, the formation of XC/C9phNBr aggregates becomes more difficult and the rate becomes slower. This implies that the process of aggregate formation is exothermic. The result is consistent with the phenomena observed by Schwuger et al., who reported that C18H37NMe3Cl can form aggregates with PEG at 298 K and with the increase of temperature the interaction between them became weaker, and there was no interaction between them at 333 K.42 3.3. Effect of XC Concentration. The effect of XC concentration on aggregation between XC and C9phNBr is indicated in Figure 5. Evidently, the concentration of XC also would affect the aggregates formation. When the concentration of C9phNBr is constant at 30 vol %, C9phNBr/XC aggregates can form in both 10 (see Figure 3D) and 15 vol % XC solution, but the rate of aggregate formation for the 15 vol % XC system is slower than that of the 10 vol % system, despite a small difference between them. It evidently implies that the lower concentration of XC does not influence the rate of aggregate formation. But when the volume concentration of XC is increased to 20 vol %, the formation of aggregates becomes difficult, suggesting that the higher the concentration of XC, the more difficult the formation of XC/C9phNBr aggregates. 3.4. The Morphology of Aggregates in Equilibrium. Figure 6 gives two typical morphologies of system C, which have been in an equilibrium state after 400 and 1000 simulation steps, respectively. To observe the shape of aggregates clearly, the

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Li et al.

Figure 4. Time evolution of the dimensionless order parameters of system C at different temperatures.

Figure 5. Time evolution of the dimensionless order parameters of 30 vol % C9phNBr at different XC concentrations.

Figure 6. XC isosurface representations of system C after 400 (left) and 1000 (right) simulation steps.

simulation cell was enlarged to be 2 repeating units in 3 dimensions. It is evident that the morphology of aggregates is rodlike or ellipsoidal after the aggregates are formed completely. According to the experimental results, XC is a rigid polyelectrolyte and it exists in the aqueous solution as a rigid rodlike shape, which has two conformations: poly-associated doublestranded helix and single molecular state.43 So the ellipsoidal shape observed in our simulations also can be regarded as an approximately rodlike shape. The appearance of two shapes perhaps is due to the two different conformations of XC. To validate the above-mentioned simulated results, the binding isotherms of C9phNBr on XC were measured (see Figure 7). The binding isotherm of the system with 200 mg‚L-1 XC shows that C9phNBr starts to aggregate on the XC chain as its concentration reaches 2.1 × 10-4 mol‚L-1, which is called a critical aggregation concentration (cac). When the concentration of C9phNBr is higher than cac, the degree of binding (β) increases quickly, implying the cooperative binding exists. However, when the concentration of C9phNBr is higher than 3.9 × 10-4 mol‚L-1, the slope of the β ∼ Cf curve decreases obviously, suggesting the binding amount of C9phNBr decreased. The reason may be the fact that the strong electrostatic attraction between C9phNBr and XC results in their association. Once a C9phNBr molecule is bound on the XC chain, other C9phNBr molecules aggregate around the C9phNBr molecule bound on XC quickly via hydrophobic interaction, so the cooperative association is observed. However, with the increas-

Figure 7. The binding isotherms of C9phNBr in different XC concentrations: (a) 200, (b) 300, and (c) 600 mg‚L-1.

ing of C9phNBr concentration the negative charges of the XC chain are gradually neutralized by the oppositely charged C9phNBr, and the attraction between XC and C9phNBr becomes weaker. The additional C9phNBr monomers have to overcome the repulsive forces between the bound and free C9phNBr to approach XC and the cooperative association effects become weaker. The rate of C9phNBr aggregating on XC decreases. In Figure 7, the cac values of C9phNBr in the solution with lower XC concentration (200 and 300 mg‚L-1 XC) remain invariable (curves a and b), which is consisted with above simulation results. As is shown in Figure 3D and Figure 5, the lower XC concentration evidently does not influence the rate of forming aggregates. The rate of forming aggregates or the time needed for C9phNBr aggregation on XC implies that the aggregate formation is easy or difficult. The faster rate shows that the C9phNBr aggregates with ease on XC. The easier aggregation means the surfactants aggregate on XC at lower free surfactant concentration. So it qualitatively confirms our simulation results that the rate of aggregate formation remains invariable. Curve c in Figure 7 indicates that the value of β at 600 mg/L XC is higher than that at 300 mg/L XC at a lower concentration

Study of Aggregation Behavior by MesoDyn Simulation of C9phNBr, but it evidently decreases as the concentration of C9phNBr is increased to more than 3.9 × 10-4 mol‚L-1. The difference is attributed to the conformation of XC. Most of the XC at 600 mg/L exists in the poly-associated double-stranded helix conformation. At lower C9phNBr concentration, most of the surfactants could be wrapped into the empty poly-associated double-stranded helix XC molecules. The relative binding amount increases with the increasing of XC concentration in aqueous solution. Therefore, it is observed that the bound amount of C9phNBr at 600 mg/L XC is larger than those at 200 and 300 mg/L XC at a lower concentration of free C9phNBr. But simultaneously the double-stranded helix associated conformation of XC via interchain cross-links results in the reduced binding sites. At higher C9phNBr concentration the additional increased C9phNBr molecules will have to overcome the repulsive forces between the bound and monomer of C9phNBr molecules to approach XC, and the normal micelles of C9phNBr start to form. So the binding becomes extremely difficult and the binding amount decreases. The simulation results indicate that the formation of XC/C9phNBr aggregates becomes difficult when the XC concentration increases to 20 vol %, and the binding isotherm shows that the bound amounts of C9phNBr on XC at 600 mg/L XC decrease, which proves simulation results agree with experimental fact. 4. Conclusions The aggregations between XC and C9phNBr in various conditions were successfully simulated with the MesoDyn method. Simulation results show that when the C9phNBr concentration is higher than 20 vol %, their aggregates begin to form. The morphology of C9phNBr/XC aggregates is rodlike or ellipsoidal. These two morphologies transform with time continuously. The formation of C9phNBr/XC aggregates becomes more difficult with increasing temperature, and the formation of aggregate is an exothermic process. The formation of aggregate depends also on the XC concentration. When the concentration of XC is higher than 20 vol %, the formation of aggregates becomes much more difficult. The simulation results are consistent with that of binding isotherms, which proves sufficiently that the MesoDyn simulation method is another important way to study the interaction between macromolecule and surfactant. Acknowledgment. The authors thank Prof. K. Shirahama (Saga University, Japan) for the present of selective surfactant electrode. We would like to acknowledge financial support for this work by the National Key Project of China (2004BA313B20), National Natural Science Foundation (20303011), and National Science Foundation (Y2004B06) of Shandong Province in China. References and Notes (1) Antalek, B.; Kowakzyk, J.; Chari, K. Langmuir 2004, 20, 11818.

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