Colloids and Surfaces A: Physicochem. Eng. Aspects 257–258 (2005) 385–390

Studies on the interaction between tetradecyl dimethyl betaineand sodium carboxymethyl cellulose by DPD simulations

Yiming Li, Guiying Xu∗, Yuxia Luan, Shiling Yuan, Zhiqing ZhangKey Laboratory of Colloid and Interface Chemistry of Educational Ministry, Shandong University, Jinan 250100, PR China

Available online 15 December 2004

Abstract

The dissipative particle dynamics (DPD) simulation method has been used to investigate the effect of pH value on the interaction betweentetradecyl dimethyl betaine (C14BE) and sodium carboxymethyl cellulose (Na-CMC) in aqueous solution. The simulation results indicate thatC14BE/Na-CMC aggregate does not form at pH = 7 (the isoelectric point pI of C14BE is 5), but at pH = 2 typical C14BE/Na-CMC aggregate isobserved, which means the interactions between them get stronger. Furthermore, at pH = 2 the curve of the end-to-end distance of Na-CMCchain as a function of C14BE volume fraction initially increases, then reduce and finally increase; while at pH = 7 its end-to-end distanceremains constant. The results of surface tension measurements are consistent with DPD simulation results. It is concluded that DPD simulationm©

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ethod can provide some important information on surfactants and macromolecules at the molecular level.2004 Elsevier B.V. All rights reserved.

eywords:DPD; C14BE (tetradecyl dimethyl betaine); Na-CMC (sodium carboxymethyl cellulose); Surface tension

. Introduction

Zwitterionic surfactants may be adsorbed onto negativelyr positively charged surface without forming hydrophobiclm and have good water-solubility and surface activity inwide pH range as well as good function of sterilization

nd biodegradation. Furthermore, the systems of zwitteri-ns mixed with ionic and nonionic surfactants show goodynergism. So zwitterionic surfactants are of importance notnly in scientific investigations but also in practical applica-

ions, such as detergency, cosmetic, medicine, food, and so on1–4]. But studies on them are far less than cationic, anionicnd nonionic surfactant, due to the difficulties in purifyingnd detecting them.

In practical applications, surfactants are often accompa-ied with macromolecules. The addition of macromoleculesould change the properties of surfactant solution. Forxample, some water-soluble macromolecules are used asnti-deposition agent in detergency, viscosity controller inosmetic, etc. So the interaction between surfactant and

macromolecule is significant[5–8]. Many technologies havbeen used to study their interaction and some usefusults are obtained[9–12]. In our previous works, the interactions between sodium bis(2-ethylhexyl) sulfosucci(AOT) and polyvinylpyrrolidone (PVP), C14BE and PVPhave been studied via fluorescence and surface tensionsurements[13–15]. Recently, computer simulations habeen widely used by chemist to explore the interactiontween surfactant and macromolecule[16–19]. DPD is anew simulation method that can give more useful infortion on surfactant system in larger length and time sc[20,21].

In solution of different pH value, Na-CMC and C14BEpresent different forms because of the existence of carbgroups. Different forms lead to different interactionstween them. So in this paper, we investigate the effepH value on the properties of C14BE/Na-CMC mixed system via DPD simulation, through which some mesoscinformation is obtained. Surface tension measurementther confirm the simulation results above. All these resindicate that the properties of C14BE/Na-CMC mixed sys

∗ Corresponding author. Fax: +86 531 856 4750.E-mail address:xuguiying@sdu.edu.cn (G. Xu).

tem are violently influenced by the pH value of the aqueoussolution.

927-7757/$ – see front matter © 2004 Elsevier B.V. All rights reserved.oi:10.1016/j.colsurfa.2004.10.120

386 Y. Li et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 257–258 (2005) 385–390

2. Computational and experimental section

2.1. Simulation model and method

DPD is a stochastic simulation technique introduced byHoogerbrugge and Koelman[22,23]and often used to simu-late complex fluid dynamical behaviors. The simulation strat-egy is to group atoms together into single “bead” and usethese centers of mass as new simulation entities. A modi-fied Velocity-Verlet algorithm[24] is adopted to integrate theNewton’s equation of motion. In the scheme, the values ofnext position, velocity and force on a soft particle are ob-tained. The positionri and momentumpi of particles can beobtained from the following equations:

dri =(pi

m

)dt (1)

dpi =∑

j

Ωijrij dt (2)

Ωij = ω(rij)

[aij + σθij − σ2

2kTω(rij)rijvij

](3)

The three terms in the square brackets of Eq.(3)are conserva-tive force, random force, and dissipative force. The latter twoforces act as heat sink and heat source, respectively, so theirc nbω

ω

m-u iatedt sedbh it isf na

a

W e-t entt tion[

a

F i.e.,C oneh wa-t meri le isc tion,C ass fac-t culea jects

the Flory–Huggins parameters between two simulated ob-jects are firstly calculated, and then they are transformed intoDPD repulsion parameters via Eqs.(4) and (5).

The simulation system contain surfactant, water, andmacromolecule in a cubic cell of size 10Rc × 10Rc × 10Rc,whereRc is the cut-off radius. The total of beads is 3000. Thespring constant between different beads is 4.0 according toGroot’s works[17]. The DPD simulation steps are usuallyequal to 10,000 in order to obtain steady and balanceableresults.

2.2. The interaction parameters

In order to calculate conservative force, the value ofaijmust be determined firstly. Here, we have obtained the inter-action parameter through the calculation of mean pair contactinteraction energy〈Eij (T)〉 between DPD particles, that is, be-tween water, polymer, hydrophilic and hydrophobic parts ofthe surfactant. In the first step, we calculate the mixing energyEmix(T) of two fragmentsi andj according to

Emix(T ) = 1

2

∑

i=j

Zij〈Eij(T )〉 −∑i=j

Zij〈Eij(T )〉 (6)

Zij is the coordinate number, i.e., the number of moleculesjw ir-i l-c

〈

P ir-i ter-a M-P r-i sev-e andc pair-i tion.

lcu-l ef

χ

wt ndi tion.S da

2

te fori acro-

ombined effect is a thermostat.aij is a maximum repulsioetween particlei and particlej, rij = rj − ri andrij = rij/|rij|.is r-dependent weight function andω(rij ) = (1− r) for r < 1,(rij ) = 0 for r > 1.Firstly, the liquid compressibility is matched in DPD si

lation, which determines the free energy change assoco density fluctuations; then the mutual solubility is expresy specifying the Flory–Huggins parameters (χ) [24]. Toave the compressibility of water at room temperature,

ound that the repulsion parameter in Eq.(3)has to be choseccording to[17]:

ii = 75kBT

ρ, ρ = 3 (4)

e have used densityρ = 3, hence the repulsion paramer aii = 25kBT . The repulsion parameter between differypes of particles is easy to obtain with the following equa17]:

ij = aii + 3.27χij, ρ = 3 (5)

or the present application, a simple model is used,14BE molecule is shown by two beads (one tail andead), which are tied together by a harmonic spring; the

er molecule is shown by one bead; and Na-CMC polyncludes 50 beads, which implies that the macromolecuomposed of 50 monomers. In different pH value’s solu14BE and Na-CMC solutions exist in different formshown inFig. 1. When the surfactant molecule, the surant head, the surfactant tail, a monomer of macromolend water molecule are considered as the simulated ob

,

hich can surround the moleculei in space. The mean panteraction energyEij (T) is obtained from Monte Carlo caulations according to

Eij(T )〉 =∫

dEijP(Eij)Eij exp(−Eij

kT

)∫

dEijP(Eij) exp(−Eij

kT

) (7)

(Eij ) represents the probability distribution of panteraction energies. The inter- and intramolecular inctions forEij (T) calculations are calculated using COASS force field[25,26]. The Boltzmann distribution of pai

nteraction energies is generated from calculations ofral thousand pairs of different molecular orientationsonformations of molecular fragments. Therefore, thenteraction energies are scaled with a temperature func

After the mixing energy between two particles is caated, the Huggins parameter (χ) could be defined using thollowing equation:

= Z∗VsEmix(T )

RT(8)

hereZ* denotes the effective coordinate number andVshe volume of one segment[27]. These mixing energies anteraction parameters can be given from Blend simulao the appropriate repulsion parameteraij could be obtaineccording to Eq.(5).

.3. Surface tension measurements

The measurements of surface tension are approprianvestigating the interaction between surfactants and m

Y. Li et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 257–258 (2005) 385–390 387

Fig. 1. Schematic structures of C14BE and Na-CMC.

molecules. C14BE was the same as that used in previousinvestigation[13]. Na-CMC (CP) and HCl (AR) were pur-chased from chemical reagent company, Shanghai (China).All solutions were prepared with triply distilled water. Thesurface tension measurements were carried out on Proces-sor Tensiometer-K12 (Switzerland Kruss Co.) using theWilhelmy-plate method at temperature of 25.0± 0.1C.

3. Results and discussion

3.1. Blend analysis

According to Eq.(6), the mixing energy for the C14BE/Na-CMC system as a function of temperature at different pHvalues is calculated. Their expressions are as follows:

pH = 2, Emix = 5.86− 0.032T − 1383

T(9)

pH = 7, Emix = 50.78− 0.035T − 1765

T(10)

From these two equations, it is found that at room tempera-ture their mixing energy is minus at pH = 2, while it is plus atpH = 7. For example, at 298 K their mixing energies at pH = 2

and pH = 7 are−8.32 and 34.43 kcal/mol, respectively. Alower mixing energy suggests that they have better stabil-ity and stronger interaction. It is obvious that the interactionbetween C14BE and Na-CMC varies with the pH value of thesolution.

The temperature (T) dependence of interaction parame-ters (χ) for C14BE/Na-CMC system at different pH values isshown inFig. 2. The physical meaning of interaction param-eter is in agreement with that of the mixing energy because itis calculated from mixing energy. A positive parameter indi-cates that the attractive interaction between C14BE and Na-CMC is weaker than that between water molecules, while thenegative value means that the attractive interaction is strongerthan that between water molecules. The lowerχ value, thestronger the interaction between them is.

It is found fromFig. 2 that at pH = 2 their interaction in-tensity (when pH = 2, Na-CMC is expressed as H-CMC) isstronger than that at pH = 7 within the studied temperaturerange. For example, from 273 to 373 K, the interaction pa-rameters at pH = 2 are between−14.5 and−13.0, while atpH = 7 they are between 64 and 45.

The interaction parameters among the surfactant’s head,the tail, water and a monomer of macromolecule at differ-ent pH value are shown inTable 1. It is seen fromTable 1

nteract

Fig. 2. Temperature dependence of i ion parameters for C14BE/Na-CMC system.

388 Y. Li et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 257–258 (2005) 385–390

Table 1The Flory–Huggins parameters from Blend simulation

χij w–w w–h w–t w–p h–h h–t t–t t–p h–p p–p

pH = 7 0.00 3.931 35. 36 99.64 −0.374 33.78 −1.545 67.13 16.99 −2.260pH = 2 0.00 25.41 35.36 99.45 −1.301 49.87 −1.545 22.94 9.702 −9.039

Here (w, h, t, p) denote water, surfactant headgroup, surfactant tail, and macromolecule.

that the interactions between Na-CMC molecule and the headof C14BE, between Na-CMC molecule and the tail are bothstronger than those at pH = 7. So the interaction between thewhole C14BE molecule and Na-CMC is stronger. It can beattributed to two reasons: the first, the headgroup of C14BEcan form hydrogen bonds with H-CMC at pH = 2; the sec-ond, the relatively crimpled H-CMC molecules have largerhydrophobicity, which makes the hydrophobic interaction be-tween them gets stronger. So C14BE molecules can easilyform aggregates with H-CMC at pH = 2, while at pH = 7 itis difficult. In addition, the headgroup’s weaker affinity forwater at pH = 2 (χhw = 25.41) also leads to their interactionwith H-CMC is strengthened.

3.2. The end-to-end distance of Na-CMC molecule

The Flory–Huggins parametersχij can be transformedinto DPD parametersaij , as shown inTable 2. Using theseparameters, DPD calculations are carried out. The simula-tions are composed of one macromolecule (50 monomers),some surfactants and water molecules in a box of size10Rc × 10Rc × 10Rc. The number of added surfactantmolecules is 1, 5, 10, 20, 33, 50, 73, 100, 200, 333, and500, respectively. To make the system equilibrate and per-mit micelles to form, these systems are simulated 104 steps( areo

T oft n iso stlyi y, andt pears( cer tionr isetN eri gt usly.A notc tweent

Fig. 3. The variation of the end-to-end distance of Na-CMC with C14BEvolume fraction.

Fig. 4 shows the interaction models in order to interpretthe strange variance of the end-to-end distance at pH = 2. AtpH = 2, most macromolecules exist in the form of H-CMCand C14BE molecules bear positive charges. In the absenceof C14BE, H-CMC molecules crimple because of theformation of intramolecular hydrogen bonds (seeFig. 4A).When a few C14BE molecules are added to the solution, as aresult of the C14BE clusters on H-CMC macromolecule areformed, the positively charged aggregates of C14BE/H-CMCextend due to the electrostatic repulsion, so its end-to-enddistance increases (seeFig. 4B). The number of C14BEclusters increases with the increase of C14BE concentration;therefore, its end-to-end distance increases gradually. Whencertain concentration of C14BE is reached, its end-to-enddistance increases to the maximum. As C14BE concentrationcontinuously increases, the hydrogen bond interactionsbetween the headgroups of C14BE clusters are dominating.So the macromolecular chain starts to crimple and itsend-to-end distance decreases (seeFig. 4C). When itsend-to-end distance reaches the minimum, more and moreclusters on macromolecule make it swell leading to itsend-to-end distance increase again (seeFig. 4D). Finally,the end-to-end distance almost keeps invariable, suggestingthat the binding of C14BE clusters on H-CMC have alreadyequilibrated.

TT

α h–h

p 23.7p 20.7

0.25s), and then the end-to-end distances of Na-CMCbtained.

The results of its end-to-end distance are shown inFig. 3.his figure indicates that at different pH, the variation

he end-to-end distance with surfactant volume fractiobviously different. At pH = 2, its end-to-end distance fir

ncreases, up to a certain point it decreases dramaticallhen it increases again until the steady balance stage apcurve a inFig. 3). But at pH = 7, its end-to-end distanemains constant within the experimental volume fracange (curve b inFig. 3). This phenomenon suggests likewhat at different pH value the interactions between C14BE anda-CMC are obviously different. At pH = 2, their strong

nteraction makes C14BE/H-CMC aggregate form, leadino the end-to-end distance of Na-CMC changes obviot pH = 7, Na-CMC’s end-to-end distance almost doeshange, suggesting that no strong interaction occurs behem.

able 2he interaction parameters in DPD simulation

ij w–w w–h w–t w–p

H = 7 25.21 37.84 140.53 350.62H = 2 25.21 108.02 140.53 350.00

h–t t–t t–p h–p p–p

7 135.37 19.95 244.38 80.53 17.614 187.98 19.95 99.97 56.70 −4.53

Y. Li et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 257–258 (2005) 385–390 389

Fig. 4. The schematic picture of C14BE/Na-CMC aggregate. (A)–(D) represent the A–D points inFig. 3, respectively.

3.3. Conformational analysis

Fig. 5 shows a typical Na-CMC conformation with 100C14BE molecules at different pH value, which are about 100and 200 ns old, respectively. Meanwhile, the mixed systemhas already equilibrated. The C14BE/H-CMC aggregates areobserved at pH = 2 (Fig. 5a); while at pH = 7 the aggregatescould not be observed and the C14BE molecules only formindividual micelle in the solution (Fig. 5b).

Fig. 6shows the aggregating process of C14BE moleculeson H-CMC chain at pH = 2. The system selected is com-posed of 100 C14BE molecules, because at this concentrationH-CMC has a smaller end-to-end distance. After 400 DPDsteps (Fig. 6a), most of C14BE molecules still exist in theform of monomer and only a few C14BE molecules aggregatearound the macromolecule. After 1600 steps (Fig. 5b), someC14BE molecules aggregate around the H-CMC molecule toform cluster and others form pre-micelle in the solution. Asteady C14BE/H-CMC aggregate finally forms at 5000 steps(Fig. 6c). It is concluded from this phenomenon that at pH = 2C14BE molecules prefer to aggregate around the H-CMCmacromolecule.

Fm nd tailo efer-e ersiono

3.4. Surface tension measurements

In order to verify simulation results above-mentioned, thesurface tension isotherms of C14BE aqueous solution withand without Na-CMC are measured at pH = 2 and pH = 7, re-spectively (Fig. 7). The pH of the solution is adjusted by HCl.Fig. 7a indicates that two inflexions are observed when Na-CMC molecules are present at pH = 2. It has been reportedthat the two inflexions in the surface tension isotherm im-plies the formation of surfactant/polymer aggregate[28,29].The surfactant concentration at the first inflexion where sur-factants start to adsorb on the polymer is referred to as thecritical aggregation concentration (cac), which is generallylower than critical micelle concentration (cmc). It is con-cluded from these facts that as C14BE concentration reachesc1, C14BE molecules start to aggregate on H-CMC chain, un-til c2 the adsorption of C14BE molecules on H-CMC chaingets saturated and normal micelles begin to form in the solu-tion. Fig. 7b shows the surface tension isotherms of C14BEaqueous solution with and without Na-CMC at pH = 7. Ob-viously, there is only one inflexion in the surface tensionisotherms whether with Na-CMC or not, suggesting that theinteraction between Na-CMC and C14BE is much weakerand their aggregate could not form. The addition of Na-CMConly decreases cmc andσcmc. At pH = 7, the behavior of Na-CMC resembles inorganic salt. When Na-CMC is added intot ue-o reakt ea asy.S ntalr t thei m-i cularc hep

lecule 00.

ig. 5. Conformations of C14BE/Na-CMC aggregate with 100 C14BEolecules. Here the red, yellow and green denote the headgroup af C14BE and macromolecule, respectively. (For interpretation of the rnces to color in this figure legend, the reader is referred to the web vf the article.)

Fig. 6. Conformations of CBE/H-CMC aggregate with 100 CBE mo

14 14

he solution they will increase the ionic intensity of the aqus solution, compress the electric double layer and b

he hydrated shell of the C14BE molecules, which induce thdsorption of C14BE molecules at the surface become eo the cmc andσcmc is both decreased. The experime

esults agree with the simulation results. It indicates thanteraction between C14BE and Na-CMC depends consungly on the pH value of the system because the moleonstitutions of C14BE and Na-CMC are influenced by tH in aqueous solution.

s present at pH = 2. The simulation steps are: (a) 400, (b) 1600, (c) 50

390 Y. Li et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 257–258 (2005) 385–390

Fig. 7. Surface tension isotherms of C14BE aqueous solution with and with-out Na-CMC.

4. Conclusions

The effect of pH value on the interaction between C14BEand Na-CMC has been studied by DPD simulations and sur-face tension measurements. The conclusions are summarizedas follows:

(1) The results of the computer simulation indicate the inter-action between C14BE and Na-CMC at pH = 2 is strongerthan that at pH = 7. So C14BE aggregate easily on Na-CMC chain at pH = 2, while not at pH = 7.

(2) The results of surface tension agree with the simulations,which there are no two inflexions in the surface tensionisotherm of C14BE aqueous solution at pH = 7; whiletwo inflexions appear in the surface tension isotherm atpH = 2, implying that typical surfactant/macromoleculeaggregate form.

(3) Computer simulation can provide some useful micro-scopic information.

Acknowledgments

The authors gratefully acknowledge financial supportfrom the National Natural Science Foundation (29973023and 20303011) and the Natural Science Foundation(Y2001B08) of Shandong Province in China.

References

[1] D.J. Liaw, C.C. Huang, H.C. Sang, E.T. Kang, Langmuir 15 (1999)5204.

[2] H. Kitano, M. Imai, K. Sudo, M. Ide, J. Phys. Chem. B 106 (2002)11391.

[3] A.B. Lowe, C.L. Mccormick, Chem. Rev. 102 (2002) 4177.[4] Z. Wang, Y. Xu, Zwitterionic Surfactants, China Light Industrial

Press, Beijing, 1990.[5] P.M. Macdonald, Y. Yue, Langmuir 9 (1993) 381.[6] G. Karlotrom, A. Carlsson, B. Lindman, J. Phys. Chem. 94 (1990)

5005.[7] J. Zajac, C. Chorro, M. Lindheimer, Langmuir 13 (1997)

1486.[8] K. Miyazawa, F.M. Winnik, J. Phys. Chem. B 107 (2003)

10677.[9] Y. Touhami, D. Rana, G.H. Neale, V. Hornof, Colloid Polym. Sci.

279 (2001) 297.[10] T. Cosgrove, S.J. Mears, T. Obey, L. Thompson, R.D. Wesley, Col-

loids Surf. A 149 (1999) 329.[11] H. Katsuura, H. Kawamura, M. Manabe, H. Maeda, Colloid Polym.

[ rf.

[ art

[ g.

[ A

[ 81

[[[[[ 18

[ 992)

[ 993)

[[[ m.

[[[ 0)

Sci. 279 (2001) 858.12] Y.X. Luan, G.Y. Xu, S.L. Yuan, L. Xiao, Z.Q. Zhang, Colloids Su

A 201 (2002) 61.13] G.Y. Xu, L. Zhang, Y.L. Yang, X.R. Huang, Spectrochim. Acta, P

A 56 (2000) 2431.14] G.Y. Xu, Y.L. Yang, L. Zhang, S.L. Yuan, G.Z. Li, Mater. Sci. En

C 10 (1999) 47.15] W.P. Sui, G.Z. Li, G.Y. Xu, C.S. Ma, J. Tang, Colloids Surf.

123/124 (1997) 473.16] S.L. Yuan, G.Y. Xu, Z.T. Cai, Y.S. Jiang, Colloid Polym. Sci. 2

(2003) 66.17] A.C. Balazs, J.Y. Hu, Langmuir 5 (1989) 1230.18] A.C. Balazs, J.Y. Hu, Langmuir 5 (1989) 1253.19] R.D. Groot, T.J. Madden, J. Chem. Phys. 108 (1998) 8713.20] R.D. Groot, Langmuir 16 (2000) 7493.21] Y.X. Luan, G.Y. Xu, S.L. Yuan, L. Xiao, Z.Q. Zhang, Langmuir

(2002) 8700.22] P.J. Hoogerbrugge, J.M.V.A. Koelman, Europhys. Lett. 19 (1

155.23] J.M.V.A. Koelman, P.J. Hoogerbrugge, Europhys. Lett. 21 (1

363.24] R.D. Groot, P.B. Warren, J. Chem. Phys. 107 (1997) 4423.25] H. Sun, J. Phys. Chem. 102 (1998) 7338.26] E. Ryjkina, H. Kuhn, H. Rehage, F. Muller, J. Peggau, Angew. Che

Int. Ed. 41 (2002) 983.27] M. Blanco, J. Comput. Chem. 12 (1991) 237.28] M. Britta, B.K. Folmer, Langmuir 16 (2000) 5987.29] K. Chari, W.C. Lenhart, J. Colloid Interf. Sci. 138 (199

593.