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Interactions between Linear Polymers and Amphiphilic Combs in Water: A Molecular Dynamics Study Tao Pan and Anna C. Balazs’ Materials Science and Engineering Department, University of Pittsburgh, Pittsburgh, Pennsylvania 15261 Received June 3, 1993. I n Final Form: September 7,199P Using molecular dynamicscomputer simulations,we examined the interactionsbetween comb copolymers, which contain hydrophobic blocks, and linear amphiphilic chains. Through hydrophobic interactions, certain combs could effectively adsorb or ”grab”specific chains from an aqueouesolution and then solubilize these chains within their hydrophobic cores. Consequently, these combs can act as “moleculartweezers”. These tweezers display a selectivity in terms of the hydrophobicity and molecular weight of the linear chains. Thus, the combs would be effective in separation processes, controlled release applications, and dispersionpolymerization reactions. Our observationsprovide guidelinesfor tailoring the comb architecture to optimize ita activity in these various applications.
Introduction Recently, there has been considerable interest in designing macromolecular structures that, through the principles of self-assembly,can act as highly selectivesieves for separation processes or behave as chemical sensors.13 For example, in a recently synthesized system (the socalled polyrotaxanes), linear copolymers could adsorb hydrophobic rings from solution by threading these rings onto the ~ h a i n . ~ * ~Other * 6 scientists fabricated rigid, cagelikestructures, which hydrophobically associate chains that display the correct polarity or range of molecular weights.6 In this paper, we consider how amphiphilic comb copolymers can be utilized to create such “smart” structures. Comb copolymers are composed of backbones and side-chains (“teeth”)that emanate from the backbone. In amphiphilic combs, the backbones and teeth can have different affinities toward the surrounding solvent. In a previous article: we examined the behavior of such combs in water and observed that the hydrophobic segments will associate or collapse, while the hydrophilic segments remain extended in solution. This behavior can be exploited to create novel structures for a variety of applications. In particular, our aim is to establish guidelines for fabricating comb copolymers that can act as “molecular tweezers”: driven by solvent-incompatibility, hydrophobic fragments in the comb would associate with or “grab” other hydrophobic segments in solution. This behavior is particularly useful for the extraction of shortchain peptides from a host fluid. Such comb copolymers would also be effective at solubilizing insoluble polymers, as is critical in dispersion polymerization. To establish these design guidelines, we examined the interactions between various combs and linear polymers through molecular dynamics simulations. Through this technique, we varied the composition of the combs and linear chains and, subsequently, determined how the extent
* To whom correspondence should be addressed.
of comb-polymer interactions is affected by these geometric factors. These studies also reveal the degree to which the combs could “distinguish” between the various linear chains in solution. The findings are useful in designing combs that display a degree of selectivity, a highly desirable property in separation processes. Below, we describe the model and the particular systems we examined.
The Model Our simulations are based on those developed by Smit et al.8to model the behavior of short surfactant chains in oil-water mixtures. (Recently, in fact, Karaborni et al. used the “Smit” model to study the solubilization of oil particles by surfactants?) The details of our model have been reported previ~usly;~ thus, here, we just provide a brief description. The system is composed of two types of particles: solvophobic and solvophilic. Following the convention employed by Smit et al.? we will refer to the solvophilic particles as “water-like” or hydrophilic, while we will refer to the solvophobic particles as ”oil-like” or hydrophobic. (This naming convention provides a convenient shorthand and does not imply that the LennardJones potentials described below provide a complete description of the intermolecular forces in water.) The comb copolymer is made up of both hydrophobic and hydrophilic particles. In particular, the comb contains a backbone that is 21 particles long and five equally spaced teeth. Unless otherwise stated, each tooth is four units in length. We consider two distinct types of combs: in the first case, the backbone is hydrophilic and the teeth are hydrophobic. In the second case, the situation is reversed: the backbone is hydrophobic and the teeth are hydrophilic. We consider the interactions between these combs and various linear chains. The length of the linear chain is fixed at 12 particles; however, we also consider one case in which the length of this chain is increased to 20 units. In these computer experiments, we also vary the ratio of hydrophobic to hydrophilic particles along the length of the chain. The comb and linear chain are immersed in 10oO single water particles. All the particles in the system interact
Abstract published in Advance ACS Abstracts, November 15, 1993. (1) Science 1993,259, 890. (2) Science 1993,260, 293. (3) See abstractsfrom session on New Macromolecular Architectures and Supramolecular Polymers Polym. Prepr. 1993,34, 50-215. (4) Wenz, G.; Keller, B. Polym. Prepr. 1993, 34,62. (5) Gibson,H.W.;Engen,P.T.;Lee,S.-H.;Liu,S.;Marand,H.;Bheda, (8)Smit, B.; Hibners, P. A. J.; Esseliig, K.; Rupert,A. M. van Os,N. M. C. Polym. Prepr. 1993,34,64. M. J. Phys. Chem. 1991,95,6361, and references therein. (6) Webster, 0. W. Polym. Prepr. 1993,34,98. (9) Karaborni,S.; van Os,N. M.;Esseliik, K.;Hilbers, P. A. J. Langmuir 1993, 9, 1175. (7) Balaze, A. C.; Zhou, 2.; Yeung, C. Langmuir 1992, 8, 2295. 0
0743-746319312409-3402$04.O0/ 0
0 1993 American Chemical Society
Comb Copolymer and Linear Chain Interactions
Langmuir, VoZ. 9, No. 12,1993 3403
through a Lennard-Jones potential given by
\
where e is the energy parameter, a is the distance parameter, rij is the distance between particles i and j , and rc is the cutoff radius. The cutoff radius is 2 . 5 for ~ the oil-oil and water-water interactions and 2% for the oil-water interactions. The latter choice ensures that the oil-water interaction is purely repulsive. In addition to this potential, there is a modified harmonic potential between the polymer units in the chain. This potential is given by
’\
p .‘a’
o.,
\
where R is\the distance between nearest neighbors along the chain. In our simulation, the force constant, k, was set equal to 30e/a2 and Ro = 1.5a. The assembly of particles is housed in a cubic box that is 12.82aunits on each side. Periodic boundary conditions are imposed in all three directions. The number density is p = 0 . 5 d . As in refs 7 and 8, the simulations are performed at constant temperature T = l . 0 d k ~and volume. At this temperature, oil and water will phase separate. In the simulation, the temperature is held constant by scaling the velocities every 50th time step.1° The Verlet algorithm” is used to integrate the equations of motion with a time step of At = 0.005a(m/e).1/2 The system reached equilibrium after approximately 30 000 time steps and the program was run for an additional90 000 time steps. (To determine when the system reached equilibrium, the total energy was monitored as a function of time. We said equilibrium was reached when there were no systematic changes in the energy.)
Results and Discussion The graphical output of the simulations allows us to visualize the conformations of the comb-polymer complex. These images are displayed in Figures 1,2,4,6,8,10,and 11. (Unless otherwise stated, the figures show the conformation of the complex at 120 000 time steps.) Further information concerning the conformation of the chains can obtained from the relevant radial distribution function gij(r). The general formula for this function is given by
where p is the number density for our system (set equal to 0.5) and nij(r) is the number of j-type particles at a distance ( r = Ar/2) to ( r + Ar/2) from an i-type particle. Thus, the function provides information on the distribution of j particles relative to the location of the i-type molecules. Here, we set Ar equal to 0.4. (The choice for the size of Ar is dictated by the condition that the number of particles within the shell 4ar2Arshould be proportional to Ar. Various values of Ar were examined and Ar = 0.4 satisfied this condition.) ~~~
(10) Heermann, D.W. Computer Simulation Methods in Theoretical Physics, 2nd ed.; Springer-Verlag: Berlin, 1990, p 31. (11) Heermann, D.W.Computer Simulation Methods in Theoretical P h y s i c s , 2nd ed.; Springer-Verlag: Berlin, 1990; p 28.
Figure 1. Interaction between the hydrophobic chain and the combwith hydrophobicteeth. The linear chain is 12 hydrophobes long. These sites are drawn as black beads. The comb contains five teeth; each tooth is four hydrophobes in length. The teeth are represented by the gray beads. The backbone contains 21 hydrophilic sites, which are represented as the white beads.
In order to compare examples that contain a different number of particles, we also calculated the normalized radial distribution functions. Here, gij(r) is divided by the total number of pairs of i-j interactions in the particular example. Figures 3,5,7,9,12, and 13 display the various radial distribution functions for the comb-polymer interactions. Each point in these plots represents a time average of the data, which was collected at every 50 steps in the interval from 100 000 to 120 000 steps. Interactions between the Linear Chain and Two Different Combs. As the first aspect of this study, we contrasted the interactions between a hydrophobic chain (all 12 particles are oil-like) and two different combs. In the first case, the comb has five hydrophobic teeth and a hydrophilic backbone. In the second case, the geometry of the comb is the same as that above; however, the backbone is now hydrophobic and the teeth are hydrophilic. Our aim was to determine which of the two combs would act as the optimal pair of tweezers, grabbing the linear chain from the unfavorable solution. In a previous study,7 we determined the conformation of the first comb in water. The chain resembles a regular micelle: the teeth associate to form a hydrophobic core and the hydrophilic backbone bends and encircles the teeth. We now consider how this comb interacts with a hydrophobic polymer. Figure 1 shows the complex that results from the comb-polymer interaction. The hydrophobic effect12drives the teeth to associate with the linear chain. This behavior is evident in the figure, where the linear chain is seen to be completely embedded within the hydrophobic teeth. Thus, the comb is highly effective at extracting this chain from the incompatible solvent and solubilizing the polymer within its micellar core. (The presence of the polymer swellsthe dimensions of the comb. In particular, in the absence of this polymer, the radius of gyration of the comb’s backbone, Rgb, was equal to 2.32 and the Rg of the entire comb, or RgC, was equal to 2 . 1 6 ~ units.7 After the polymer is incorporated into the hydrophobic domain, Rgb = 3.44 and R e = 3.62. These values were measured after the chain reached its equilibrium structure.) (12) Tanford, C. The Hydrophobic Effect; Wiley Interscience: New York, 1980.
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Figure 2. Interaction between the hydrophobic chain and the comb with a hydrophobic backbone. The structure of the comb is the same as in the above figure; however, the backbone is now hydrophobic and the teeth are hydrophilic. The hydrophobic chain is again drawn in black, the hydrophilic teeth are white, and the hydrophobic backbone is gray. 1.o
u TEETH:OIL m--~
BACKB0NE:OIL
0.8
- 0.6 CU X I h
Figure 4. (a,top) Interaction between linear chain that contains six hydrophobes and six hydrophiles and the comb with five hydrophobic teeth. Each tooth is four hydrophobee long. The symbols for the teeth and backbone are the same as in Figure 1. (b, bottom) Interaction between linear chain that contains two hydrophobes and ten hydrophiles. The hydrophobic sites on the polymer are drawn as black heads, while the hydrophilic sites are represented as white beads.
2 . 0,
0.4
0.2
0.0 0.0
-
1.o
2.0
3.0
4.0
Figure 3. Normalized radial distribution functions between the linear hydrophobic chain and the hydrophobic components of the two different combs.
Our earlier studies on the second type of comb showed that the hydrophobic backbone collapses and the hydrophilic teeth extend into the water, the entire assembly resembling an inverse mi~elle.~ Figure 2 shows a typical image of the complex that is formed when this second comb and the hydrophobic chain interact. While the chain is situated near the hydrophobic backbone, the chain appears less localized within the comb than in the first example. (The Rg of the comb’s backbone is none-theless increased by the interaction with the linear chain. In particular, in the absence of the polymer, Rgb = 1.48: while Rgb = 3.56 when the polymer is present. As a consequence, the Rg of the entire comb is increased from 2.447 to 4 . 7 0 ~units.) Figure 3 showsthe radical distribution function between the hydrophobicspecies on the comb and the linear chain for the two different cases described above. (The distribution functions have been normalized to account for the fact that there are 20 tooth sites but 21 backbone sites.) Sincethe value of the function is higher at shorter distances for the comb with the hydrophobic teeth, we can conclude that this comb is more effective at localizing and, thus, securing the linear chain. (Recall that the radial distribution effectively measures the probability of finding a second molecule at r given there is a molecule at the origin. Thus, a higher value of gii(r) at fixed r indicates that the molecules lie closer together.) The linear chain is itself
collapsed in the poor solvent (see Figures 1 and 2) and, thus, can more readily overlap with multiple, short hydrophobic segments than one, longer hydrophobic block. While the unfolding of the chain would be energetically compensated by associating with the longer hydrophobic backbone, such alignment would be entropically unfavorable. Interactions between Comb and Various Linear Chains. We now focus on the interactions between the comb with the hydrophobic teeth and various linear chains. We observed above that this comb is effective at grabbing a hydrophobic chain. Our next goal was to determine how effective this comb could be a grabbing other less hydrophobic polymers. These studies will reveal the degree to which the comb can distinguish between different chains in solution and selectively adsorb a limited or specific class of polymers. To carry out these investigations, we considered the interactions between the comb and a chain that contains six hydrophobic and six hydrophilic sites. We also examined the comb’s interactions with a chain that contains only two hydrophobes, with the remaining 10 particles being hydrophilic. Figure 4 shows typical conformationsof the combs and polymers in solution for the two new cases described above. (These are to be contrasted with the image in Figure 1, where the chain is entirely hydrophobic.) Figure 4a shows that the comb and diblock copolymer do, in fact, interact: some of the hydroprobes in the chain are associated with the hydrophobic teeth. Thus, the comb can still grip onto this chain. Note, however, that the hydrophilic segment of the chain extends into the favorable solvent and away from the comb.
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Comb Copolymer and Linear Chain Interactions
--
1.o
I
12 HYDROPHOBES HYDROPHOBES 2 HYDROPHOBES
H6
0.0
1.o
2.0
3.0 r
1.o
0.8
4.0
1
-
TEETH:4
H LONGER TEETH:7
+--+
LONGER LINEAR POLYMER:20
5.0
(in CT units)
Figure 5. Radial distributionfunctionsbetween the entire linear chain and the teeth sites in the comb for the various cases examined. The numbers in the legend refer to the number of hydrophobes in the linear chain.
Figure 6. Interaction between linear hydrophobic chain and comb that contains five hydrophobic teeth, where each tooth is seven hydrophobes long. Symbols for the linear chain, teeth, and backbone are the same as in Figure 1.
The situation is quite different in Figure 4b: there is no overlap between the comb and the chain that contains only two hydrophobes. In effect, the chain is sufficiently hydrophilic that it is soluble in the surrounding water; consequently, the chain is not driven to bind to the hydrophobic domain within the comb. (Solvent compatibility is also reflected in the structure of the chain: the polymer in Figure 4b is far more extended than the hydrophobic chain in Figure 1.) A more quantitative description of these results is given in Figure 5, where we plotted the radial distribution functions between the hydrophobic teeth and the three linear chains we examined. As can be seen, the functions become less peaked as the number of hydrophobes in the chain decreases. In the last case described above, the function appears rather flat. Increasing the Length of the Hydrophobic Teeth. We also investigated whether the gripping attributes of the comb could be enhanced by increasing the length of the hydrophobic teeth. One might anticipate that increasing the number of hydrophobicunits within the teeth would enhance or promote hydrophobic interactions. To test this hypothesis, we increased the length of all five teeth to seven oil-like particles. Figure 6 shows the conformation of the complex that results when this new comb interacts with the chain that is 12 hydrophobeslong.
r (in ounits)
Figure 7. Normalized radial distribution functions between the linear hydrophobic chains and the various hydrophobic teeth. (The first two numbers in legend refer to the length of the hydrophobic teeth.)
Further insight into this system can be found by referring to Figure 7, where we compare the normalized radial distribution functions for the case of the short teeth and these longer teeth. (Here, each gij(r) is divided by the total number of pairs of teeth-chain interactions in the respective system.) At short distances, the values for the short teeth lie above the numbers for the long teeth. This indicates that the short teeth are, in fact, more effective at localizing the hydrophobic chain. In the case of the longer teeth, the hydrophobic species are sufficiently long that they can undergo intramolecular association in order to avoid the unfavorable solvent (see Figure 6). Thus, they are less driven to form a tight intermolecular cluster. Furthermore, the system is too crowded for the teeth to form a narrowly confined hydrophobic domain. In fact, the chain no longer resembles a simple micellar structure. Here, in interacting with the dispersed teeth, the linear chain is relatively more stretched than in Figure 1. Furthermore, Figure 6 shows that association with the dispersed teeth brings the linear chain into contact with the hydrophilic backbone. Thus, the specificity between the linear chain and the teeth is diminished in this example. An important question to consider is whether the long teeth would, in fact, be more effective if these species were less crowded within the comb. To answer this issue, we retained the teeth at the outer edges and at the middle of the backbone; however, we removed the other two sidechains. The comb now contains three teeth, which are eight units apart. Each of the teeth are seven units in length; thus, there are a total of 21 hydrophobic sites. Note that there are 20 hydrophobic sites in the comb with the five shorter teeth. Thus, by comparing the results from these two examples, we can also address the following question: Given approximately the same number of hydrophobes, which arrangement is more effective at adsorbing this linear chain: multiple, short teeth or fewer, but longer teeth? Figure 8a, which shows the complex that results when the linear chain interacts with this three-toothed comb, readily provides an answer to the above question. As is clearly seen, the linear chain lies outside of the hydrophobic domain. The reason for this behavior can be understood by studying images from earlier time steps, such as that in Figure 8b, which reveals the conformation of the complex after 80 000 time steps. The image shows that the longer,
3406 Langmuir, VoZ. 9, No. 12,1993
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Figure 10. Interaction between the linear hydrophobic chain, which contains 20 hydrophobic sites, and the comb that contains five hydrophobic teeth, each of which are four sites long. The symbols for the linear chain, teeth, and backbone are the same as in Figure 1.
Figure 8. Interaction between the linear hydrophobic chain and the comb that contains three hydrophobic teeth, where each tooth is seven hydrophobes in length. Part a (top) shows the complex after 120 000 time steps, while part b (bottom) shows the cluster at 80 000 steps. The symbols for the linear chain, teeth, and the backbone are the same as in Figure 1.
O--O
o.8
t t
-m- 0.4 h
0.0
Figure 11. Interaction between the linear hydrophobic chain, which contains 20 hydrophobes, and the comb with three hydrophobic teeth, where each tooth is seven hydrophobes in length. The symbols for the linear chain, teeth, and backbone are the same as in Figure 1.
5 TEETH, LENGTH 4
.----..3 TEETH, LENGTH 7
h
I\
I \
1.o
I
2.0 3.0 r (in (r units)
4.0
-
-
5.0
Figure 9. Normalized radial distribution functions between the linear hydrophobic chain and the hydrophobic teeth on the various combs.
flexibleteeth form a loose cage, which does not significantly constrain the polymer. Thus, the chain can easily “fall outn,which, in fact, occurred at the later time step (Figure 8a). Consequently, we can conclude that the comb with multiple, short teeth forms a tighter cage in which to confine the chain and, thus, is more optimal for trapping this relatively short polymer. This observation is also supported by the radial distribution functions in Figure Ssince the curve for the five-toothed comb is significantly higher than that for the three-tooth case.
Increasing the Length of the Hydrophobic Chain. Since the chain with the short hydrophobic teeth is effective at localizing a relatively short hydrophobic chain, it is of interest to consider how this behavior would change if the length of the linear chain were increased. Consequently, we examined the interaction between our reference comb and a linear chain that is 20 hydrophobes long. Figure 10 shows a typical conformation of this combpolymer complex, while the normalized radial distribution for the teeth-polymer interactions is plotted in Figure 7. Both images reveal that the comb is less effective at localizingthis longer chain. The long polymer is relatively spread out (see Figure 10) since there are too many hydrophobic particles in the system to pack tightly into a small domain. In fact, comparison of the teeth-polymer versus backbone-polymer radial distribution functions reveals the curve involving the backbone lies above the plot describing interactions with the teeth. In effect, the linear chain is wrapping around the entire comb. Again, the specificity between the linear chain and the hydrophobic teeth has been decreased. From our findings on the three-toothed comb, we could hypothesize that this architecture, with the enhanced tooth length and spacing between the teeth, would be more effective at localizing the longer polymer. We, in fact, find that this comb is no more effective than the fivetoothed species above. Figure 11shows that the polymer
Langmuir, Vol. 9, No. 12,1993 3407
Comb Copolymer and Linear Chain Interactions 10
-
-
t . 5 TEETH, LENGTH 4 3 TEETH, LENGTH 7 08
6
C--.
FIVE TEETH SEVEN TEETH
i
1 00 : 00
' -
'
10
20
30
4.0
50
r (in a units)
Figure 12. Normalized distribution functionsbetween the linear chain that is 20 hydrophobes long and the hydrophobic teeth on the various combs. is not entangled within the hydrophobic teeth and the radial distributions function is very similar to the one for the five-toothed species (see Figure 12). However, these studies provide further insight into the behavior of combs with long teeth and confirm our observations from the previous section. By studying the images from previous time steps and Figure 11, we again find that the long teeth are too "floppy" to form an efficient trap. The chain can easily diffuse between the flexible "bars" and fall out of the loose hydrophobic domain. Thus, short teeth, which are more rigid (and cannot readily bend to form intramolecular associations), are preferable to the longer teeth. From these findings, we can infer that a comb with a longer backbone and more short teeth (spaced at the same intervals as in our smaller comb) could be effective at grabbing the longer polymer. To test this hypothesis, we examined the interactions between a 20-site hydrophobic polymer with a comb whose backbone was increased to 28 hydrophobes to accommodate seven short (four-site) hydrophobic teeth. As can be seen from Figure 13, the comb with the longer backbone and more, short teeth is more effective at adsorbing the longer polymer than either the comb with five teeth or the three longer teeth (Figure 12).
Conclusions We considered the interactions between amphiphilic comb copolymers and linear chains in solution. We observed that certain combs could effectively adsorb or "grab" specific chains from the aqueous environment and then solubilizethese chains within their hydrophobic cores. The efficiency of this operation depends not only on the comb architecture but also on the hydrophobicity and length of the chain. The comb with five short oil-like teeth was particularly effective at solubilizing the chain that contained 12 hydrophobes. The five teeth created a hydrophobic cage, which engulfed the linear species. This geometry was more effective than the comparable comb that contained a hydrophobic backbone and hydrophilic teeth. We increased the length of all five teeth, which gave rise to significant steric hindrance between these fragments.
DISTANCE (in the units of 0)
Figure 13. Normalized distribution functions between the linear chain that is 20 hydrophobes long and the hydrophobic teeth on the various combs.
Due to these steric interactions, the teeth could not form a distinct cagelike structure. Consequently, this comb was less effective at localizing the hydrophobic chain. The comb with only three long teeth was also ineffective at grabbing the chain: though the steric effects were eliminated, the teeth were too floppy to form a rigid trap. Our findings indicate that combs with short teeth, which are less flexible, provide the preferably architecture for trapping chains. The comb with five short hydrophobic teeth was, however, less effective at localizing more hydrophilic chains. Optimal comb-polymer overlap occurs when the length of a hydrophobic block within the chain is comparable to or longer than the comb's hydrophobic teeth. The extent to which the polymer was solubilized within the hydrophobic core also depended on chain length. The comb with the short teeth could solubilizethe shorter chain and, yet, could not pick up the longer polymer. Our results point to the fact that increasing the length of the backbone and adding more short teeth (while keeping the spacing between the teeth comparable to the tooth length) provides an effective architecture for adsorbing longer chains. In this manner, the combs can be tailored to adsorb chains within specific ranges of molecular weight. In summary, the results show that these combs can act as molecular tweezers, picking up amphiphilic chains in solution. Such combs display a selectivity in terms of the hydrophobicity and molecular weight of the chains. Thus, the combs would be effective in separation processes for oliopeptides, for examples. In addition, such combs can effectively solubilize chains that are solvent-incompatible. This behavior is important for drug delivery or controlled-release applications, as well as in dispersion polymerization reactions. Our observations provide guidelines for tailoring the comb architecture to optimize its activity in these various applications.
Acknowledgment. A.C.B. gratefully acknowledges financial support from the National Science Foundation, through Grant Number DMR-9107102, the Department of Energy, through Grant Number DE-FG02-90ER45437, and The Dow Chemical Company.
