Salt Effects on Sol–Gel Transition of Telechelic Polyelectrolytes in

Article pubs.acs.org/Macromolecules

Salt Effects on Sol−Gel Transition of Telechelic Polyelectrolytes in Aqueous Solutions Ran Zhang,†,‡ Tongfei Shi,*,† Lijia An,† and Qingrong Huang§ †

State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, P. R. China ‡ Graduate University of the Chinese Academy of Sciences, Beijing, 100049, P.R. China § Food Science Department, Rutgers University, 65 Dudley Road, New Brunswick, New Jersey 08901, United States

ABSTRACT: Using Monte Carlo simulation techniques, we focus on the physical gelation behavior and conformation change under the existence of additional monovalent salt, which provides screening to the electrostatic interaction of charged telechelic polyelectrolyte chains and causes new balance between hydrophobic interaction of end groups and electrostatic interaction originated from the polyelectrolyte blocks. For the electrostatic interaction dominated system, the screening effects will decrease the electrostatic repulsion between small sized clusters and enable the further aggregation of TP chains, resulting in prompting the sol−gel transition progress; for the short-range attraction dominated system, the screening effects present a complicated phenomenon, which includes the prompting effect at the beginning of sol−gel transition and a hindering effect when the gelation progress is close to an end.

1. INTRODUCTION Telechelic polyelectrolytes, referred as TP, a special associating polymer containing short blocks at both ends, have many novel properties as well as wide applications compared with neutral telechelic polymers,1−7 which can be attributed to the specialty of polyelectrolytes. Unlike neutral polymers, when dissolved in water, the ionogens on the polyelectrolyte chain will ionize into charged groups and counterions carrying opposite charges. Therefore, the interaction becomes more complicated, and factors like concentration, pH and salt addition will undoubtedly affect the association behaviors. The addition of salt provides screening for electrostatic interaction, which might induce: a significant influence the chain conformational8−12 and dynamic properties;13 an ion-bridging effect and rapid flocculation when multivalent salt ions are involved;14−16 the dissolving17,18 and forming19 of polyelectrolyte complexes, phase separation,20,21 and swelling/collapsing of charged gels.22−25 For the chemical gels, polyelectrolytes are cross-linked together by covalent bonds and most of the attention has been paid on the swelling behavior of the gels, which certainly depends on the ionic condition in the solution.22,26−33 The kinetics process24,29 as well as the structure21,22,30,34,35 of © 2011 American Chemical Society

swelling of polyelectrolyte gels can be quite different with the variation of salt conditions, and the net charge as well as the concentration of gelling polyelectrolytes is of great importance for the free ions to provide osmotic pressure for swelling;31,32 the gel structure may also influence the uptake of salts in the gel matrix.22 It was pointed out that not only the salt concentration but also the species of salt may cause different effects on the swelling behavior of polyelectrolyte gels.23,33 Theoretical21,22,24,36−38 and simulation25,39 studies have investigated the effects of salt addition on cross-linked polyelectrolytes gels thoroughly, which bring our understanding of the mechanisms of gel swelling under salt conditions to a microscale level. However, for the physical gelation of charged polymers, the situation is more complicated since the cross-linking points in the gel network are maintained by hydrophobic interactions, hydrogen bonds, entanglements of chains or other noncovalent connections, which are reversible under certain conditions and find use in fields like drug delivery systems.40−44 The additional Received: August 18, 2011 Revised: December 1, 2011 Published: December 22, 2011 555

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Polyelectrolyte monomers are monovalent and carrying negative charges. Salt ions, explicitly simulated in the solution, are monovalent hard spheres with the same diameter as the chain monomers. The positive salt ions act as counterions for the polyelectrolyte monomers, and the number of cations equals to the number of anions and the polyelectrolyte monomers to maintain the charge neutrality. The solvent is implicitly treated as a dielectric continuum. When there is no salt added, the solution contains Nt chains and Nc counterions, the salt ions will be added into the solution at certain percentage f of the monomer charges. Thus, there will be N=NA Nt+ Nc(2+ f) nodes in the solution. The attraction potential between hydrophobic monomers Uattr is an attractive LennardJones potential

salt ions may screen the electrostatic interactions and cause phase separation6,45,46 or the forming of a physical gel.6,30,46,47 For this complicated charged polymer system, theory and simulation work will be helpful for understanding the mechanism of its physical gelation. In the early years Vasilevskaya et al. established a simple model of telechelic polyelectrolytes in solution with additional salt and investigated the association behavior of TP under different solvent qualities and salt concentration;6 and their theoretical prediction was quickly proved by experimental results.45 In Vasilevskaya’s work, under a hydrophobic interaction energy εh ≥ 12kBT, which can be viewed as the hydrophobic interaction dominated system in our work,48 the sol−gel transition (phase separation) field became wider when increasing salt concentrations; however, until now a relevant explanation of this phenomenon in the microscale is still missing. In the former papers we have studied the TPs’ gelation behavior in salt-free solution and provided proper explanation of their physical gelation behavior with the analysis on chain conformation and cluster forming.48,49 If salt is added to the TPs solution, the dissolved salt ions will interact with the charged monomers and to some extent affect the chain conformations, so that the forming of clusters and even physical gelation process will be influenced. Our early results indicated the competition between hydrophobic and electrostatic interaction dominates the solution properties. When the hydrophobic interaction is relatively strong and favors the aggregation, electrostatic repulsion provides its contribution by maintaining a spacial structure, resulting in a much lower gelation concentration close to ϕ* (the overlapping concentration, acquired by viewing the TP chain as a homogeneous polyelectrolyte chain in solution).48 Meantime, loop to bridge transition is witnessed with the increase of concentration, in agreement with the experimental studies.2,50 The additional salt ions in the solution will undoubtedly screen the electrostatic interaction and bring the competition to a new balance. Unfortunately, there are few systematic references on these. In this paper, using Monte Carlo simulation techniques, we focus on the effect of additional salt ions on the association behavior of chains and on the reason for so-called extending of sol−gel transition in TP solutions. The simulation model we use is described in the next section, and after that we present our discussion of simulation results and the conclusion remark. It is found that the extending of so-gel transition happens only when relatively strong hydrophobic interaction dominated in the system. The complicated phenomenon involves the saltprompting effect at the beginning of sol−gel transition and a salt-hindering effect when the gelation progress is close to an end. On the other hand, when there exits relatively weak hydrophobic interaction, only the salt-prompting effects on the sol−gel transition progress results in the sol−gel transition in a lower concentration range without the behavior of extended sol−gel transition, which is not mentioned in any theoretical predictions.

⎡⎛ σ ⎞12 ⎛ σ ⎞6 ⎤ Uattr = 4εattr ⎢⎜ attr ⎟ − ⎜ attr ⎟ ⎥ ⎝ r ⎠ ⎥⎦ ⎢⎣⎝ r ⎠

(1)

where εattr is the association energy. The interaction between other pairs is represented by the repulsive L-J potential:

Urep

⎛ σrep ⎞12 ⎟ = 4εrep⎜ ⎝ r ⎠

(2)

where εrep is the repulsive energy. Here σattr = σrep = σ = 1 and the cutoffs of these L-J interactions is 2.5σ. According to the Ewald method, the expression of Coulomb potential Uelec,tot is

Uelec , tot = kBT λBEtot

(3)

Etot = Er + Ek + Es + Ed (4) where kB is the Boltzmann constant, T refers to temperature, the Bjerrum length λB is defined as the distance at which two unit charges have the interaction energy kBT and has the expression λB = e2/(4πεoεrkBT). λB can be considered as a measure of the strength of electrostatic interactions vs the thermal energy and is equal to 7.14 Å for water at room temperature. Er and Ek on the right of eq 4 are the contributions from the real space and the Fourier space, Es is the self-term, and Ed is the dipole-correction term.51 These potentials are: Er =

Ek =

1 2

∑ ∑ qiqj i,j

erfc(α|rij + nL ⃗ |) |rij + nL ⃗ |

n⃗

⎛ 1 1 4π 2 k2 ⎞ ⎜ ⎟|ρ̃(k ⃗)|2 − exp ∑ 2 2 2 πL3 ⃗ ⎝ ⎠ α 4 k k ≠0

α Es = − π

(5)

(6)

N

∑ qi 2

(7)

i=1

2π

N

| ∑ q ri |⃗ 2 (1 + 2εs)L3 i = 1 i (8) In eq 6 the reciprocal vector k⃗ = 2πn⇀/L, n⃗ = (n1,n2,n3):nt ∈ Z. In eq 8 εs is the dielectric constant of the medium surrounding the sphere. How to manipulate the Coulomb sum using a Monte Carlo style is given in the appendix of ref 49, and here the measure we take is exactly the same. The simulation work is done in the NVT (constant particle numbers, constant volume and temperature) ensemble Ed =

2. MODEL AND SIMULATION DETAILS This model resembles the one we used in the former paper.49 In a cubic cell (L = 48σ) with periodic boundary conditions in 3 dimensions, the TP chain has a structure ANA−BNB−ANA containing 20 monomers, with NA  1 and NB  18. Block A stands for the hydrophobic groups, and block B a flexible hydrophilic polyelectrolyte with bond length fixed at 1.1σ. 556

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according to the Metropolis algorithm. Salt ions including counterions randomly move with a sphere range of diameter D = 10σ in one MC trial. As for the chains, we use several algorithms for relaxation. These algorithms, such as pivot,52 translation,53 kink-jump, and crankshaft54 are very efficient in accelerating the simulation and promoting the convergence of potentials. In a pivot move, a chain node is chosen at first, splitting a chain into halves, then the shorter part moves around the chosen node; in a translation, the shorter part just take an even move without breaking the bond connecting the node. Crankshaft and kink-jump are very much alike in pattern: we define an axis by choosing two unconnected nodes in a chain, and let the nodes between the chosen ones move round the axis. The main difference between these two methods is that in a kink-jump only one node is moving.

3. SIMULATION RESULTS 3.1. Comparison between Salt-Free and Saline Systems. We have considered the effect of TP concentration on their sol−gel transition behavior in an earlier work48 and found that the competition between hydrophobic interaction and electrostatic interaction has a major effect on the distribution of chain association fraction: with strong hydrophobic interaction energy, the short-range hydrophobic attraction dominates the system, while the electrostatic interaction provides a contribution to the formation of gels by maintaining a spacial swelling structure; when the hydrophobic interaction energy is relatively low and the electrostatic interaction dominates, increasing concentration can screen electrostatic repulsion in some degree,55−57 which makes for the growth of clusters and the sol−gel transition at a higher concentration. Vasilevskaya et al.6 found that the overlap concentration (ϕ*) is decreased with the increase of salt concentration, associative gels are formed in TP solution accompanied by supernatant phase; with greater ϕ, the gel phase the supernatant phase disappears. While in theory and simulation studies, percolation model is widely used58−60 and fits well in the situation of determining the sol−gel transition.48,49 When a certain amount of salt ions are added into the system, the electrostatic repulsion of TP chain is weakened, which causes a significant difference in the percolation value P(ϕ) (see Figure 1). For simplicity, the sol−gel state is defined as the concentration area when 0 < P(ϕ) < 1, while P(ϕ) = 0 for the sol and P(ϕ) = 1 for the gel state. The dashed fitting line of the simulation data shows the percolation curve of a TP solution with a salt concentration ϕs = 0.008, while the solid line stands for the salt-free system. The hydrophobic interaction energy (ε=εattr/kBT) is set at 8, under which the aggregation of chains is favored. It is obvious that the screening from salt ions presents a major influence on the sol−gel transition: the addition of simple salt ions at ϕs = 0.008 causes a broadened sol−gel transition area (from 0.013 < ϕ < 0.018 to 0.010 < ϕ < 0.022) compared with the salt-free case, which was predicted in Vasilevskaya’s theoretical work.6 Here we extend the understanding of this phenomenon to a molecular level by investigating the fraction of the four basic association types of TP chains49 (free, loop, dangling and bridge), which is shown in Figure 2a. The aggregation of chains due to comparatively strong hydrophobic attraction are well represented by the fast increasing of f loop(ϕ) and decreasing of f free(ϕ) with increasing ϕ; f bridge(ϕ) increases significantly with greater ϕ and f loop(ϕ) starts to decrease after reaching a maximum, which indicates

Figure 1. Percolation probability (P) plotted against the concentration ϕ at different hydrophobic interactions (a) ε = 8; (b) ε = 5. The saltfree data is shown in solid line to guide the eye, while the salt-added data is shown in dashed line.

Figure 2. Chain association type fraction ft(ϕ) as a function of concentration ϕ at different hydrophobic interactions (a) ε = 8 and (b) ε = 5, where “t” stands for the type of chains. The salt-free data is shown in solid, while the salt-added data is in hollow and dashed.

the loop to bridge fraction transition during the sol−gel transition progress.2,50 The additional salt will undoubtedly decrease f free(ϕ) and fdangling(ϕ), due to its screening effect on the charged blocks; it is also found that the additional salt causes f loop(ϕ) to reach its maximum at a smaller ϕ with a higher value than the salt-free case; however, as for f bridge(ϕ), the salt effect is not monotonic with ϕ, with ϕs = 0.008 the value of f bridge(ϕ) is higher than the salt-free one with increasing 557

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ϕ at the beginning, but becomes lower when ϕ further increases. This could be viewed that salt effect could be different for different period of gelation, also, it could be considered that the contribution of electrostatic interaction to the gelation of TP is different with increasing ϕ. When ϕ is low, the electrostatic repulsion hinders the aggregation of chains, the addition of salt ions can make for the interchain and intrachain (forming a loop) aggregation by electrostatic screening, which interprets the difference of f loop and f bridge between the salt-free system and the system with a salt concentration at lower ϕ. When ϕ increases, a continuous gel structure forms under the sustaining of electrostatic repulsion. The addition of salt ions, however, will cause screening to this sustaining force and reduces f bridge. Thus, gel structure will form at higher ϕ. Now we go back to Figure 1b. When ε = 5, electrostatic interaction is relatively strong and hinders the association of chains, increasing concentration is necessary for the physical gelation progress of the salt-free system, since more polyelectrolyte blocks and their counterions in solution can give rise to additional electrostatic screening and bring down the effective electrostatic interaction distance. This is why the sol−gel transition happens at a much higher concentration area than the one under ε = 8. The effect of additional salt can be obviously concluded to be identical with the one on the beginning of sol−gel transition in Figure 1a: the fitted percolation line of the system with a salt concentration is just ahead of the one of salt-free system in polymer concentration (from 0.028 < ϕ < 0.04 to 0.026 < ϕ < 0.038), without any broadening effects. The corresponding fraction of chain association types in Figure 2b indicates that the comparatively strong electrostatic interaction has a major effect on the fraction of chain types. For the solid lines representing the salt-free system, the slow decreasing of f free(ϕ) with increasing ϕ and the considerable amount of dangling chains in the system suggest the stretched nonloop conformation of chains; f bridge(ϕ) and f loop(ϕ) increase slowly with increasing ϕ, indicating the hindered aggregation due to electrostatic repulsion. The dashed lines representing the system with ϕs = 0.008 remain almost the same trend with the solid curves but only at lower concentration, suggesting the salt effects on relatively weak hydrophobic systems favor the aggregation of chains, without causing the screening to the sustaining force of gel structure. By combination of theoretical and simulation approaches, de la Cruz et al. also predicted that the addition of monovalent salt will bring the onset of TP gelation to a lower polymer concentration, despite using different criterion on determining gelation.61 In further comparison with their simulation results, we discuss the effect of salt on the distribution of cluster size at different polymer concentrations (see Figure 3). When ε = 8, for ϕ = 0.0109 in the sol state, the additional salt at ϕs = 0.008 causes a wider distribution and larger cluster size compared with the salt-free case; for ϕ = 0.0163 in the sol−gel coexisting state, the increase of size of salt-induced larger cluster is more significant; when it comes to the gel state at ϕ = 0.0253, the additional salt causes the cluster size reaching its maximum (there are 140 chains in the corresponding system) with a narrower distribution than the salt-free case, suggesting almost all the TP chains are involved in the forming of gel network. When ε = 5, for the sol state at ϕ = 0.0253, the cluster size is small with a narrow distribution both for the salt-free and the saline system. The salt screening effect becomes significant

Figure 3. Distribution of cluster size with different concentrations, three typical concentrations are chosen to present the additional salt effects on sol, sol−gel, and gel state. W(M) = N(M)/[N(1) + N(2) + ... + N(N)], N(M) is the number of cluster of size M.

when the concentration rises to ϕ = 0.0362 in the sol−gel coexisting state; the distribution of small cluster size is maintained, but a broad peak representing the size distribution curve of large clusters in the saline system appears compared with the salt-free curve. When ϕ = 0.0398 in the gel state, again, the size distribution of small clusters shows no significant changes; the broad peak representing large size clusters of the salt-free system appears, and the presence of salt results in larger cluster size and a higher value of distribution function. In general, the effects of added salt ions are identical though different simulation box lengths and descriptions of salt ions are used.61 3.2. The Salt Effects on the Gel Structure. In Figure 3, the additional salt produces a major effect on the clusters formed in the system, especially in the sol−gel transition area. This influence could be reflected clearly by the snapshots in Figure 4 of the corresponding concentrations. Compared with the cluster in Figure 4a, with additional salt the one in 4c increases in size significantly, even forms temperate percolation across the simulation box. Similar phenomena can be found in Figure 4, parts b and d, under ε = 5, at higher concentration and greater cluster size. There are more differences between the systems under ε = 8 and ε = 5, which might not be described with only observation of the snapshots. A series of statistic measurements is needed for deeper understanding of the gel structure. The salt effects on the gel structure can be demonstrated by the correlation function gAA(r) of the hydrophobic monomers in Figure 5. At ϕ = 0.0146 and ε = 8 (see Figure 5a), the system has just entered the sol−gel transition field. The additional salt causes an increase of gAA in the middle range (5 < r < 15), indicating the aggregation of chains are more favored due to screened electrostatic repulsion. The correlation peak (as the arrow points) in the long-range shifts to smaller r with the addition of salt, suggesting the correlation distance between micelles is reduced by the screening of salt ions. This phenomenon is also witnessed when the system enters the gel state (see Figure 5c). For ϕ = 0.0325 and ε = 5 (see Figure 5b), the system is also in the sol−gel transition field. However, 558

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Figure 4. Snapshots of clusters formed in systems with/without additional salt ions. (a) ϕ = 0.0163, ε = 8, ϕs = 0; (b) ϕ = 0.0362, ε = 5, ϕs = 0; (c) ϕ = 0.0163, ε = 8, ϕs = 0.008; (d) ϕ = 0.0362, ε = 5, ϕs = 0.008. The hydrophobic monomers are shown in red, and the polyelectrolyte block in green color. The salt ions (including counterions), single chains, and other small clusters are not shown for clarity.

Figure 5. Effect of salt on the correlation function gAA(r) of hydrophobic monomers: (a) ϕ = 0.0145, ε = 8; (b) ϕ = 0.0325, ε = 5; (c) ϕ = 0.0253, ε = 8; (d) ϕ = 0.0398, ε = 5.

gAA in the middle range (5 < r < 10) presents a decrease due to the addition of salt, and the correlation peak (as the arrow points) in the long-range shifts to a larger r, indicating the correlation distance between micelles is a little increased; with additional salt, a significant increase of gAA around r = 2 is captured both at ϕ = 0.0325 and ϕ = 0.0398, while for the latter the system enters the gel state, similar shift of correlation peak in the long-range is also captured (see Figure 5d). The differences in correlation function suggest that the salt effects on system structure under relatively strong and weak hydrophobicities are different. This difference can be interpreted by further investigation of the micelle structure. Nb, the average number of branches of micelle,62−64 presented an increase with the additional salt ions (see Figure 6, parts a and b). For ε = 8, Nb shows no further increase with ϕ when ϕ > 0.0145; with additional salt Nb rises

from 2 to 4 at lower concentrations, but does not show much rising when ϕ increases, especially in the sol−gel transition field. For ε = 5, Nb increases with ϕ during the whole concentration range compared with ε = 8; with additional salt Nb rises apparently in the sol−gel transition field, which causes the micelles to grow bigger in size. This could explain why the correlation distance of micelles under small ε exhibits an increase with the additional salt. Nm, the average number of micelles in the system is investigated in Figure 6, parts c and d. At low ϕ, the screening effects of addition of salt favor the aggregation of chains, causing a little increase of Nm for both ε = 8 and ε = 5; as ϕ increases, the additional salt causes a decrease of Nm for both ε = 8 and ε = 5 due to increased Nb, especially for ε = 5. The developing of gel structure with ϕ can be viewed as the increasing of Nb and Nm. For ε = 8, Nb shows no further 559

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Figure 6. Effect of salt on the average branch number of micelles (Nb) and the average number of micelles (Nm). ε = 8 for (a, c); ε = 5 for (b, d).

increase with ϕ when ϕ > 0.0145, which means the growing of gel structure is mainly attributed to the increase of Nm. However, the additional salt causes a decreased correlation distance between micelles, which obviously requires a larger Nm to develop the gel structure. These interpretation coincides with the analyses of association types of chains in section 3.1, that the additional salt screens the sustaining force among the gel network and causes a higher gelation concentration and therefore an extended sol−gel transition area at ε = 8. While for ε = 5, both Nb and Nm present an increase with greater ϕ during the sol−gel transition field. The additional salt induces a larger Nb and therefore an increased micelle size, which would neutralize the negative effects caused by the relatively slower increase of Nm with additional salt ions. Thus, the extending of sol−gel transition would be avoided, and the additional salt provides a promoting effect in the gelation process under relatively weak hydrophobic interaction. 3.3. Effect of ϕs on Association Types of Chain. The above simulation results provide us the comparison of salt-free system and saline system with a specific salt concentration, ϕs = 0.008. Next, it is essential to take salt concentration ϕs as a variable to investigate the association behavior of TP. For the hydrophobic interaction dominated system (ε = 8), two TP concentrations corresponding to the sol and gel state (ϕ = 0.0109 and ϕ = 0.0253) are chosen to study the salt effects on chain association. Figure 7 presents the chain association type fraction f t(ϕs) as a function of ϕs. As a whole, at ϕ = 0.0109 and ϕ = 0.0253 the system is mainly involved with loop and bridge chains due to strong hydrophobic attraction. In the sol state (Figure 7a), chains tend to form flowerlike micelles at first,2,48,50 f loop(ϕs) increases with the increasing of ϕs, suggesting the screening effect favors the forming of these micelles; a further increase of ϕs causes f loop(ϕs) to decrease and f bridge(ϕs) to increase, indicating these micelles are further connected to form clusters or so-called multicore micelles.65 After ϕs = 0.01, f loop(ϕs) and f bridge(ϕs) show no significant changes with ϕs, there are also a few free chains and dangling chains at the beginning, which decrease to 0 with the increase of ϕs. In Figure 7b, due to the already connected gel structure,

Figure 7. Chain association type fraction f(ϕs) as a function of salt concentration ϕs at different TP concentrations for the hydrophobic interaction dominated system. ε = 8, (a) ϕ = 0.0109; (b) ϕ = 0.0253.

there are few free or dangling chains left when no salt is added. Increasing ϕs will result in the screening of electrostatic repulsion; therefore, f bridge(ϕs) shows a decrease and f loop(ϕs) an increase with ϕs, and both of them show no significant changes when ϕs > 0.005. For weaker hydrophobic interaction (ε = 5), i.e., the electrostatic interaction dominated system (see Figure 8), the influence of ϕs to the association behavior of TP chains, as concluded above, is improving aggregation by screening electrostatic repulsion. ϕ = 0.0253 and ϕ = 0.0398 are chosen corresponding to the sol and gel state. In the sol state (Figure 560

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further increase with ϕ when ϕ > 0.0145, and the additional salt does not induce a significant increase of Nb, but causes a decrease to the micelle correlation distance. With increasing salt concentration, for the hydrophobic interaction dominated system, the prompting and hindering effects are very significant for the sol state and gel state separately; for the electrostatic interaction dominated system, the prompting effects works for both the sol and gel state.

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AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]. Telephone: +86-431-85262137. Fax: +86-431-85262969.

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ACKNOWLEDGMENTS This work is supported by the National Natural Science Foundation of China (20734003, 21174146, 51028301) Programs and the Fund for Creative Research Groups (50921062); the Special Funds for National Basic Research Program of China (2009CB930100, 2010CB631100).

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REFERENCES

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Figure 8. Chain association type fraction f(ϕs) as a function of salt concentration ϕs at different TP concentrations for the electrostatic interaction dominated system. ε = 5: (a) ϕ = 0.0253; (b) ϕ = 0.0398.

8a), when no salt is added, chains mainly exist as frees and danglings, with a small number of bridges and loops; with the increase of ϕs, f free(ϕs) decreases due to increased screening effects, while fdangling(ϕs), f bridge(ϕs), and f loop(ϕs) show an increase with ϕs. In the gel state (Figure 8b), when no salt is added, bridge and dangling chains are more favored, with only a few free and loop chains left. f free(ϕs) decreases, while both f bridge(ϕs) and f loop(ϕs) show an increase with ϕs. The dangling chain increases with ϕs in the sol state but decreases in the gel state. This is because dangling chains act as intermediates: free chains change into dangling chains and the latter into loops and bridges during the sol−gel transition.49

4. CONCLUSION In this paper, using Monte Carlo simulation techniques we continue our work on the association behavior of telechelic polyelectrolytes in the presence of small salt ions. We found the additional salt has different contributions to the aggregation of TP chains. For the system dominated by electrostatic interaction, the screening effects will decrease the electrostatic repulsion and enable further aggregation of chains, resulting in prompting the sol−gel transition progress to a lower concentration area than the salt free system; for the system dominated by hydrophobic attraction, the additional salt causes a widened sol−gel transition field: the screening effects favor the aggregation of chains, resulting in the prompting effect of sol−gel transition, but cause a decrease in the sustaining force of gel structure and a higher gelation concentration. A thorough investigation of the gel structure provides a clearer mechanism that how the additional salt influences the gelation process: for the electrostatic interaction dominated system, Nb increases with ϕ during the concentration range, with additional salt both Nb and micelle correlation distance increase; while for hydrophobic interaction dominated system, Nb shows no 561

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dx.doi.org/10.1021/ma201872e | Macromolecules 2012, 45, 555−562