Morphology and Dynamics of Catenanes in Dilute Solutions

MORPHOLOGY AND DYNAMICS OF CATENANES IN DILUTE SOLUTIONS

AND AT LIQUID/LIQUID INTERFACE

A Thesis

Presented to

The Graduate Faculty at the University of Akron

In Partial Fulfillment

Of the Requirements for the Degree

Master of Science

Saeed Akbari

December, 2018

MORPHOLOGY AND DYNAMICS OF CATENANES IN DILUTE SOLUTIONS

AND AT LIQUID/LIQUID INTERFACE

Saeed Akbari Thesis

Approved: Accepted:

______Advisor Dean of the college Dr. Mesfin Tsige Dr. Ali Dhinojwala

______Committee Member Dean of the Graduate School Dr. Andrey Dobrynin Dr. Chand Midha

______Department Chair Date Dr. Tianbo Liu

ABSTRACT

Catenanes as mechanically interlocked polymers possess distinct, well-defined topological interactions and, as a result, exhibit a variety of unique properties. Template- directed synthesis is responsible for the high yield syntheses of these structures40.

However, little is known about the interfacial and physical properties of this class of polymers. As proved many times in other polymeric systems, Molecular dynamics simulation can be used to characterize them. Among the limited studies, Wang, et.al quantified the influence of topological constraints on the structural and dynamic behavior of different topologies of ring polymers. They found that catenane topologies have larger flexibility than any of the single chain systems, indicative of the larger structural deformations that these large complexes can sustain53.

We will present simulation results on the morphology and dynamics of linear, ring and catenane polymers in dilute solutions. Pure poly (ethylene oxide) (PEO), pure polystyrene

(PS) and diblock of PEO and PS catenanes in a select group of solvents are examined. The effect of solvent quality on morphology and dynamics is also investigated. Flexibility caused by different polymer type, different chain structure and different interaction of chains with solvents has the dominant role in determining morphological and dynamical properties of the polymers. The behavior of diblock catenane at an interface of two immiscible solvents provided interesting morphological and dynamical understanding. An interesting dynamics of the two blocks, both translational and rotational, has been observed

iii at the liquid/liquid interface. At the interface, the flexibility of the rings also plays a major role in relative rotation of the rings.

ACKNOWLEDGEMENTS

First of all, I wish to express my sincere gratitude to my advisor, Dr. Mesfin Tsige, for his guidance and help throughout my 2-year-graduate study. I feel extremely lucky to work closely with him. I have learned a lot from him, not only on various aspects of molecular dynamics simulation, but also on how to be a hard working person.

Then I also would like to thank Dr. Andrey Dobrynin for his helpful comments as my committee member.

I also would like to thank my group members, Iskinder Arsano, Dr. Selemon Bekele and

Alankar Rastogi for being my great friends and kindly helping me with the research.

Last but not least, I would like to thank my wife and my parent for their love, support and encouragement.

TABLE OF CONTENTS

Page LIST OF TABLES ...... vii LIST OF FIGURES ...... viii CHAPTER I. INTRODUCTION ...... 1 II. SIMULATION METHODS ...... 8 III.STRUCTURAL PROPERTIES OF PEO AND PS IN DIFFERENT TOPOLOGIES 15 3.1 Rg plots of various topologies ...... 19 3.2 VMD images of various topologies...... 21 IV. DYNAMICAL PROPERTIES OF PEO AND PS IN DIFFERENT TOPOLOGIES 28 4.1 Translational diffusion and global rotation ...... 30 4.1.1 peo (wat): ...... 30 4.1.2 peo (tol): ...... 33 4.1.3 ps (wat): ...... 34 4.1.4 ps (tol): ...... 35 4.1.5 Hetero catenane at Liquid/Liquid interface...... 40 4.2 Relative rotation ...... 42 V. CONCLUSION ...... 45 REFERENCES ...... 47 APPENDIX ...... 53

LIST OF TABLES

Table Page

Table 1. Rg2 values for different group of samples based on different topologies for last 4 ns of NVT simulation...... 17

Table 2. Relative rotation of rings of catenanes at various frame intervals and at the entire 4 ns of simulation for a) homo catenanes and b) hetero catenanes...... 43

vii

LIST OF FIGURES

Figure Page Figure 1 Synthesis of poly[n]catenane 3 via assembling 1 and 2 into a metallosupramolecular polymer (MSP), followed by ring-closing to yield a poly[n]catenate (i.e., metallated poly[n]catenane) and demetallation40...... 3

Figure 2. Plateau heights H for the linear, isolated ring, 2-ring catenane assembly, and other ring structures. H is a measure of deformability or flexibility of the system53...... 6

Figure 3. Cartoon and VMD images of constructed ps topologies as (a) linear chain, (b) ring, (c) catenane comprising two identical interlocked rings, and (d) hetero catenane comprising two different interlocked rings...... 10

Figure 4. Scheme of peo/ps hetero catenane at water/toluene interface. In this figure toluene solvent is in the upper portion of the box while and water is in the lower portion of the box. The green ring is peo and the blue ring is ps...... 12

Figure 5. Rg2 plots of a) peo and b) ps at Liquid/Liquid interface of ps/peo hetero catenane during 20 ns of NVT simulation...... 16

Figure 6. Rg2 plots of a) peo (wat), b) peo (tol), c) ps (wat), and d) ps (tol) in last 4 ns of NVT simulation. In all cases green line is for linear chain, red is for ring, blue is for homo catenane and purple is for hetero catenane...... 20

Figure 7. VMD images of a) peo/peo (wat) and b) peo/peo (tol) ...... 22

Figure 8. Three representative snapshots of solvated peo at zero _top., small _mid., and large _bottom. pulling force. Hydrogen bonds between water molecules and peo oxygen atoms are marked through dashed lines68...... 23

viii

Figure 9. VMD images of ps/ps (wat) and ps/ps (tol). In order to clearly see the collapsed and expansion mode of the ps rings, the backbone images are also included. a1) backbone of ps/ps (wat), a2) ps/ps (wat), b1) backbone of ps/ps (tol), and b2) ps/ps (tol) ...... 24

Figure 10. VMD images of peo/ps (wat) and peo/ps (tol). In order to clearly see the collapsed and expansion mode of the ps rings, the backbone images are also included. a1) backbone of peo/ps (wat), a2) peo/ps (wat), b1) backbone of peo/ps (tol), and b2) peo/ps (tol) ...... 25

Figure 11. Rg2 plots of peo and ps of peo/ps hetero catenane at liquid/liquid interface. In this figure, red line is for ps, and blue line is for peo...... 26

Figure 12. 3D plot of center of mass motion in the simulation box during 20 ns NVT simulation for a) peo/ps hetero catenane at water/toluene interface and b) peo/peo catenane at toluene...... 29

Figure 13. a) Translational motion and b) global rotation of various topologies of peo in water. In both cases green line is for linear chain, red is for ring, blue is for homo catenane and purple is for hetero catenane...... 31

Figure 14. Translational motion of peo/peo (wat), ps/ps (wat), and peo/ps (wat) hetero catenanes. In this figure, red is for peo/peo (wat), blue is for ps/ps (wat) and gray is for peo/ps (wat)...... 32

Figure 15. a) Translational motion and b) global rotation of various topologies of peo in toluene. In both cases green line is for linear chain, red is for ring, blue is for homo catenane and purple is for hetero catenane...... 33

Figure 16. a) Translational motion and b) global rotation of various topologies of ps in water. In both cases green line is for linear chain, red is for ring, blue is for homo catenane and purple is for hetero catenane...... 34

Figure 17. a) Translational motion and b) global rotation of various topologies of ps in toluene. In both cases green line is for linear chain, red is for ring, blue is for homo catenane and purple is for hetero catenane...... 35

Figure 18. a) Translational motion and b) global rotation of linear chain of ps in water and toluene. In both cases, red is for toluene and blue is for water ...... 39

Figure 19. Translational motion of peo in a) water and b) toluene. In both cases green line is for linear chain, red is for ring, blue is for homo catenane and purple is for hetero catenane...... 39

Figure 20. Translational motion of various topologies of a) peo and b) ps in toluene. In both cases green line is for linear chain, red is for ring, blue is for homo catenane and purple is for hetero catenane...... 40

Figure 21. Translational motion of a) peo in water, toluene, and Liquid/Liquid interface and b) ps in toluene and Liquid/Liquid interface. In both cases, red is for toluene, blue is for water and gray is for Liquid/Liquid interface...... 41

Figure 22. Global rotation of a) peo in water, toluene, and Liquid/Liquid interface and b) ps in toluene and Liquid/Liquid interface. In both cases, red is for toluene, blue is for water and gray is for Liquid/Liquid interface...... 42

CHAPTER I

INTRODUCTION

As the field of macromolecular and supramolecular chemistry continue to grow, the focus has begun to shift from single molecules of increasing complexity to macromolecular assemblies composed of individual components that can be designed and constructed to behave in concert to perform more complicated functions. Such Supramolecular assemblies could find a great application as the basis for molecular machines that pioneering work of Stoddart, Sauvage, and Feringa about them won the 2016 Nobel Prize in Chemistry1. Catenanes are one of these macromolecular architectures where instead of chemical bonds, topological bonds connects the molecular elements. Catenanes are not solely synthetic; nature utilizes the "links in a chain" format in DNA and protein catenanes2-5, building up linked chains to form the "molecular chainmail" found in viral capsid structures6-8. Investigations in the past have probed whether or not DNA nanomachines can be constructed from these biological catenanes9-11, but the most promise remains in synthetic constructs designed with chemical moieties specific to a desired interaction or type/range of motion. The morphology and dynamics of catenanes are controlled by chemistry of its rings and topological constraints in their mechanically interlocked rings. In fact, the structure and dynamics of rings are significantly different from their linear counterparts due to the absence of free ends in the rings. Pasquino, et.al12 experimentally measured the linear rheology of polyisoprene, polystyrene, and poly (ethylene oxide) rings and discovered that ring structures have a universal trend completely different from their linear counterparts. Moreover, considering rings as the elements of a catenane, morphological and dynamical

1 properties are governed by the presence of mechanical bonds, an important class of topological interactions, rather than covalent bonds13. Realized potential applications of catenanes range from sensors14-17 to molecular memory and nanoswitches18-20 to motors, rotors and actuators21-24. The primary barrier to adoption of catenanes has historically been synthesis: early efforts used blends of preformed macrocycles and linear chains, with subsequent cyclization of the linear components. Statistically, some of the linear chains were likely to thread cyclic components before their own cyclization to create interlocked structures. This "statistical approach," used in the 1960s and 1970s, was and remains useful for creating interlocked macromolecules of arbitrary polymer species that can be cyclized. Early yields for catenanes from these processes were extremely low25-30, far less than 1% for [2]catenanes, and production of any longer chains would have been limited to a tiny fraction of even that amount. Later, Schill and co-workers 31 used a method in which components to be mechanically bonded would first be covalently bonded, with the covalent tethers between components removed after the cyclization of the linear component. Though covalent-directed synthesis improved yields significantly versus statistical methods, yields remained small and essentially relegated work on MIMs to a novelty in synthesis until the early 1980s, when Sauvage’s CuI-phenanthroline methodology 17;32 brought metal-directed passive template (PT) approaches to the fore, marking the first major advance in catenane synthesis: methods to hold interlocking sub-units in place while cyclization reactions are completed to create interlocked macromolecules, rather than rely on statistical methods. Furthermore, template-directed synthesis significantly increased the yields of catenanes versus covalent-directed and statistical approaches, and higher yields made it possible to verify the synthesis of larger catenanes by making the inclusion of multiple cyclic groups more efficient. Among template-directed methods, metal-directed passive template PT approaches have some shortcomings. In this approach in order to exclude oligomerization, polymer chains should be in a high dilution solution. Furthermore, it is expected to have efficient threading owing to the presence of sufficiently stable precursor complex, however, the cyclization happens slowly.

Recently Lewis, et.al33 has invented a new method which is called active template (AT) approach. This approach has the capability of solving many of mentioned problems and facilitate catenane synthesis with a high yield. They introduced AT Cu-mediated azide

alkyne cycloaddition (ATCuAAC) approach for a high-yielding synthesis of

[2]catenanes. In this multicomponent approach there are precursors which are very small to be able to cyclize directly. However, they undergo successive reactions until the interlocked rings obtained by a final AT-CuAAC reaction. More recently, however, schemes to synthesize effectively infinite inorganic [n]catenanes have been reported in the literature34;35 although still rare, and similar approaches for organic catenanes are gaining traction36-39. For organic catenanes, linear poly[7–27]catenanes, branched poly[13–130]catenanes, and cyclic poly[4–7]catenanes have been synthesized recently by Wu et .al40 and represent the longest extant organic catenanes. As it is depicted in Figure 1, Wu’s approach had a preassembly of a metallosupramolecular polymer (MSP) as a template. Then it had an efficient ring closing reaction and a demetallation of the produced metallated poly[n]catenane. This successful MSP template strategy could achieve a high yield of 75% for synthesis of main chain poly[n]catenanes.

Figure 1 Synthesis of poly[n]catenane 3 via assembling 1 and 2 into a metallosupramolecular polymer (MSP), followed by ring-closing to yield a poly[n]catenate (i.e., metallated poly[n]catenane) and demetallation40.

In addition to basic equilibrium structure or conformation in solution, the topic of catenane adsorption on surfaces has received considerable attention recently. The ability

3 to attach catenanes to surfaces is expected to be an important area of focus for the creation of complex molecular-level devices41, not only for their ability to act as molecular motors based on rotational freedom, but also for applications in sensory devices, where rotational changes in adsorbed catenanes can be converted to signals to monitor changes at the surfaces of diagnostic equipment. In the case of molecular machinery such as sensors, motors and actuators, as well as molecular memory devices, the dynamics of the components are of critical importance. From the basic mobility of components to the range of motion available to components to the reversibility of effects caused by environmental changes and the time scales over which such changes take effect and can be reversed, component mobility influences many aspects of application, and system structure influences component mobility. For instance, in a catenane-based switch, a redox reaction may be able to give the impetus for the flip of the switch, but knowledge of how quickly the switch changes state or the degree of hysteresis involved in each cycling of the switch is important to arresting or enhancing the ring rotation in concert with the intended application. In long-chain catenanes, internal motion in the rings may have important implications for polycatenane diffusion or reptation, where internal dynamics can access modes of movement not available to linear chains. The adoption of template-directed synthesis has opened the door for the inclusion of many new structures and chemical moieties into mechanically interlocked assemblies. Novel assembly methods often lead to complex assemblies for which little is known about the ultimate physical properties. Here, the community can benefit from a robust contribution from computational simulation; as new and more versatile synthetic methods unlock possibilities for new catenanes, simulation can be used to characterize physical properties for targeted application. Electronics applications lend themselves to characterization via ab initio and density functional theory (DFT) methods 18;24;42–44, while dynamics, structure, packing, and mechanical properties are best approached through molecular dynamics 44;45. Key to MD simulation is the force field, which defines the set of functions and parameters used to represent the energies of the different interatomic interactions. A number of MD force fields have been used to study small catenanes. Ratner, Schatz and

4 colleagues used the MM3 force field 46–48 in several studies to simulate the folding of oligorotaxanes51;52 and to further calibrate the force field using DFT calculations on the nature and extent of hydrogen bonding and − stacking in [3]catenanes 44. Ceccarelli, et.al49 used the well-known AMBER 86 force field alongside rare-event sampling to study the switching mechanism in catenanes with multiple stable states. Beyond the need to characterize small catenanes, simulations are also valuable in the evaluation of possible properties in catenanes with more mechanical bonds mentioned previously. Some small catenane systems have been investigated via all-atom MD and Monte Carlo (MC) 3;4;49; 50–53, and all-atom/coarse-grained methods54–57 can provide critical access to physical behavior and scaling laws for larger structures/denser systems like polycatenanes. Simulation studies on catenanes to date have primarily focused on [2]catenanes, and most simulations have focused on topological conformations of interlocked ring macromolecules such as DNA catenanes2–4;58 and their implications on molecular topology59;60. Specialized all-atom MD simulations have been used to study switching in [2]catenanes49. Rane and Mattice61 performed Monte Carlo simulations to investigate static and dynamic properties of polyethylene oxide (PEO) [2]catenanes and compare them with unlinked cyclic PEO while Pakula and Jeszka62 has attempted to treat main-chain poly[n]catenanes of length 10 or more. Recently, Rauscher57 has used coarse-grained simulation to compute dynamics of polycatenenes with 25 rings. Information on catenane conformations and dynamics is expected to come primarily from MD simulations. Recently Wang, et.al53 studied the configurational behavior and dynamics of ring polymers in various supramolecular topologies. They used molecular dynamics simulations to investigate the effect of topological constraints on the morphological and dynamical behaviors of ring polymers within supramolecular assemblies. As it is demonstrated in Figure 2, their results demonstrated that an isolated ring has lower flexibility than a linear chain. This behavior is due to the successive relaxation of topological constraints. In fact, due to the relaxation of the ring structure, the configurational ensembles are limited relative to the linear chain.

Figure 2. Plateau heights H for the linear, isolated ring, 2-ring catenane assembly, and other ring structures. H is a measure of deformability or flexibility of the system 53.

Wang, et.al53 also discovered that catenane structures have larger flexibility than any of the single chain systems. The reason is that catenane can sustain larger structural deformations. Furthermore, these interlocked rings can have larger configurational ensemble. They analyzed the rotational diffusivity of catenanes and interestingly discovered that a catenane with 24-mer rings possess a rotational diffusivity three times more than a catenane with 50-mer rings. They figured out that for larger rings, the structural entanglement of the two interlocked rings provides collapsed configurations that disfavor free rotation. In fact, in catenanes of larger rings, the larger intrachain structural ensemble makes that structural entanglement. As mentioned earlier, Rauscher, et.al57 performed molecular dynamics simulation to investigate unique dynamical properties of a poly[n]catenanes. Their results indicated that at short length scale, the dynamics of poly[n]catenanes are slowed comparing to isolated linear polymers. They related it to the mechanical bond within catenanes. Since similar behavior have been detected in a melt of linear chains owing to the entanglement, they also considered the slow dynamics a consequence of an entanglement-like effect. The main motivation of the ongoing research on catenanes is that still there is little knowledge about the physical properties of catenanes. With increased control over catenane components and the ways in which they come together, catenanes become an entirely new polymer architecture to explore, much like ring, star and comb polymers in the past. However, before we can move toward more complex investigations of catenane melts or glasses, or long catenanes or catenanes under confinement, as is the current interest

6 in other known architectures, we must start with the basic properties of small catenanes, working to establish a more complete background as a basis for further investigations. In many simulation studies, the goal is to characterize or predict the properties and behavior of compounds already synthesized. In this initial investigation, we seek to characterize known catenanes or catenanes that are currently possible through known synthetic means. As newer methods of synthesis and their resulting structures are discovered, all-atom simulations will be invaluable to characterizing structure and dynamics, especially the coupling of intramolecular and intermolecular dynamics on the overall system. In the first phase, single homo polymer [2]catenanes have been studied in solution. This phase of the study will be extended to investigation of hetero catenanes: diblock [2]catenanes composed of individual rings of a given species (e.g. a polystyrene ring interlocked with a poly(ethylene oxide) ring)— hereinafter collectively referred to as hetero catenanes. Both homo catenanes and hetero catenanes are studied in this first phase in order to better understand the effects of multiple polymer species in catenated rings (homo catenation and hetero catenation effects). The main goal is to determine how the structure and dynamics of chains are affected by the quality of solvent(s) and polymer characteristics with respect to the molecule topology. The second phase will focus on structure and dynamics of hetero catenanes at liquid/liquid interfaces. Much of the potential for application of polymers of different architectures arises from their interfacial properties — adhesion, lubrication, coating, stabilization of micellar or colloidal suspensions, modification of interfacial tension between phases, chain ordering and microstructural evolution at interfaces, separation in blends, etc. Whereas the behavior of a given polymer in a single solvent phase is comparatively straightforward, how a given polymer in solution reacts to a second solution phase (difference in solvent quality), addition of an interface is a critical field of investigation for well-known polymer architectures, and much more so for lesser-known ones like catenated polymers. Therefore in this phase, we seek to extend our study of hetero [2]catenanes in solution to their structure and dynamics at liquid/liquid interfaces. These two phases use all-atom MD simulation to give the most accurate characterization of the effects of solvent(s) and interface on the structure and dynamics of [2]catenanes.

CHAPTER II

SIMULATION METHODS

The Molecular dynamics (MD) simulations are performed with all-atom peo and ps structures in polar solvent water and in non-polar solvent toluene and at water/toluene interface. We are well aware that All-atom (AA) simulations could become more difficult for very large systems or for dynamics expected to take place over very long time scales. Ceccarelli, et.al49 all-atom studies clearly highlights the inherent size limitations of such detailed simulation methods. Pakula and Jeszka62 suggested that main-chain [n]catenanes with a sufficient number of macrocycles (or, presumably, other component architectures) should appear similar to linear polymers with macrocyclic "monomers", but with the system sizes that would be necessary to test this hypothesis, quantum-level or all-atom simulations would prove infeasible even on current top-performance supercomputer systems. In the case of the work by Ceccarelli, et.al49, the mechanism of catenane switching occurred on the order of microseconds, so the method of action-derived dynamics was used in order to extend the accessible time scale of all-atom MD. Without extraordinary resources, all-atom MD is generally capable of accessing time scales on the order of tens of nanoseconds, from a time step in the range of a few femtoseconds. This is sufficient for our work which is about single-molecule simulations in a solvent. For dense polymeric systems or larger molecules (more rings/more mechanical bonds) with complex architectures and interactions, dynamics on the order of microseconds can be expected, in which case all-atom simulation becomes largely untenable. In such cases, coarse-grained (CG) models can be used to represent whole monomers or multiple monomers as super

8 atomic units. This coarser representation of the system reduces the number of degrees of freedom and smooths over much of the fastest motion present, extending the range of accessible simulation times and system sizes. CG models preserve the overall topology of polymers but inevitably lose details of specific chemical interactions in more detailed models. Therefore, all-atom MD is required especially in this research where the possible hydrogen bonding between hydrogen atoms of water molecules and oxygen atoms of peo has a very crucial role in understanding morphological and dynamical properties of the catenanes. The OPLS-AA (Optimized Potentials for Liquid Simulations All Atom) force field is used for peo, ps and toluene and SPC/E model is employed for water. In practice, OPLS- AA is a well-developed force fields for simulations of catenanes, especially for relatively short catenane lengths. Molecular dynamics simulations were conducted using LAMMPS simulation suite63. The time step for numerically integration of classical equation of motion through Velocity Verlet algorithm was 1 fs. Initially, in order to get the desired density of the dilute solution in the box, 1ns of simulations were conducted in the NPT ensemble with keeping temperature at 300 K using a NoséHoover thermostat64 and pressure at 1 bar using a NoséHoover barostat64.

Then 20 ns of NVT simulation at constant density and 300 K was performed to cover equilibration time and sampling period of the simulation. In 4ns the temperature, pressure, energy and size of the chains stabilized. The 16 ns sampling runs were performed after equilibration runs and the last 4ns of data were used for analyzing morphological and dynamical properties of each system. The system snapshots were collected every 2ps and used for analysis through in-house codes developed in JAVA and VMD65 was employed for visualization of the polymer configurations. Different topologies of polymer chains such as linear, isolated rings and interlocked rings are constructed to investigate the ring, homo catenation and hetero catenation effects. The initial topologies of the polymer chains were constructed with the help of Avogadro software66. Scheme of these four different topologies are illustrated in Figure 3:

Each constructed topology was placed inside a cubic box and solvated by water molecules or toluene. All polymer chains were solvated such that the dilute solution reaches a concentration of 0.01. For different chains in the two different pure solvents, periodic boundary condition with box side length between 10 and 15 nm was applied in all three dimensions to prevent direct interactions of the chains through these periodic boundary conditions. For Liquid/Liquid interface, box dimensions of 11*11*22 nm were made. Each ring in a catenane has 60 monomers and the atomistically detailed representation would be (CH2CH2O)60 for the peo rings in the catenanes and (C8H8)60 for the ps rings in the catenanes. In order to investigate the effect of Liquid/Liquid interface on structure and dynamic of the catenenes, a simulation box consists of the two immiscible solvents is constructed that provides a precise Liquid/Liquid interface between water and toluene. Then the hetero catenane of peo/ps was located at the interface layer. The reason that the catenane was not initially located inside one of the pure solvents was because it would take long time for the catenane to be able to move toward the interface. In order to observe the effect of poor solvent in the case of ps, the hetero catenane was located at interface in a way that ps ring was inside water and peo was inside toluene. Interestingly, within a few hundreds of picoseconds the ps ring of the hetero-catenane turned around and located inside toluene while peo ring moved to interface and stayed there during the duration of the simulation. In fact, ps moved to toluene because it is a good solvent for ps and peo moved to the interface since it has no preference between water and toluene which are both good solvents for peo. A schematic view of the final position of peo/ps hetero catenane at water/toluene interface is illustrated in Figure 4.

To quantify the size of the 60-mer peo and ps polymers as a function of their topology, radius of gyration (Rg) of the polymers in water, toluene and at water/toluene interfaces was computed. In homo catenanes this Rg is the average size of the two identical rings. Rg of the samples is employed as a representative of their morphological properties. In the case of dynamics, based on the topologies, two different types of properties are analyzed. For all of the constructed structures, translational motion of chain’s center of mass and global rotation of chains are probed. For rings in the catenanes, intramolecular rotational diffusion which is demonstrated by relative rotation of each ring with respect to the other ring is investigated. For computing translational motion and global rotation of the chain structures, time averaged mean-square displacement (MSD) of all chain atoms was calculated. For the translation, the center of mass displacement was investigated while for global rotation, the

MSD of all atoms of the chain was calculated after a translational alignment of the centers of mass of the two configurations. Practically, for the translation and rotation, the MSD of each single chain (linear, isolated ring and different rings of a hetero catenane) was calculated. But for homo catenane the average MSD of the two identical rings was obtained and compared with MSD of the other single chains. Computation of the relative rotation as opposed to global rotation of the chains required a precise approach to be employed. In fact, for relative rotation, the constituent rings within catenanes can rotate relative to one another such that while the relative position between the rings is changed the overall catenane structure stays unchanged.

The first step in the computation approach was to compute structural distances di,j between all two successive configurations i and j in our simulation time. Using the rotationally minimized root mean-square deviation (RMSD) between the atom coordinates, 53 the di,j of chains in catenanes is computed . In practice with the help of Kabsch algorithm, a translational alignment of the centers of mass of i and j at the relative 3D rotation is applied on this RMSD distance that can minimizes this distance. In fact, Kabsch algorithm can separate the elements of the configurational changes between frames in the chain through singular value decomposition. When comparing two successive frames, these elements can be swelling or collapse or rotation of the chain at one frame with respect to its configuration at previous frame. Then only the rotation element of the configurational changes was selected and employed to compute the minimized RMSD distance. Since catenanes are interlocked rings and in ring structures the constituent monomers are indistinguishable, therefore it was required to determine an arbitrary origin on the circular contour of the ring backbone. Then it was possible to index the atoms of the polymer backbone in the first frame and identify the indexing of contour atoms in the second frame that minimize the configurational dissimilarity between two frames under all possible indexing of backbone atoms. The Kabsch algorithm was applied to calculate the RMSD between two successive frames of two ring catenanes in a way that the RMSD was minimized over translation of center of mass, spatial rotation and indexing of 60 monomers in each ring. In order to optimize the permutational indexing of each ring, all 602 indexing

13 ways should be probed. However, since the time interval between the successive snapshots is 2 picosecond, small indexing rotation was expected therefore it was possible to do fast probe over local permutations. It was found that probing ±10 shifts in the indexing is enough to detect the optimal indexing and therefore calculate the least amount of RMSD. Large structural changes in the rings could prevent the capability of clear detection of relative rotational motions within the RMSD calculations. However, in literature53 the calculated relaxation time for a similar polymer ring was in excess of ∼100 picosecond while the delay between successive frames in our work is 2 picosecond which is much shorter than the that relaxation time. Therefore, it can be concluded that at this short time intervals, conformational flexibility of rings did not influenced our ability to detect the relative rotation of rings, precisely.

CHAPTER III

STRUCTURAL PROPERTIES OF PEO AND PS IN DIFFERENT TOPOLOGIES

In this study, in order to make sure that the sampling was done after equilibration of the system, the Rg2 values were traced from the beginning of NVT simulation and it demonstrated that after around 1ns the Rg2 plot did not show any significant change and in general fluctuated around an equilibrium value. As a representative of all samples, figure 5 illustrates the Rg2 of peo and ps of peo/ps hetero catenane at the Liquid/Liquid interface of water and toluene for entire 20 ns of NVT simulation. The more flexible peo ring shows more fluctuations in Rg2 than the rigid ps ring.

Figure 5. Rg2 plots of a) peo and b) ps at Liquid/Liquid interface of ps/peo hetero catenane during 20 ns of NVT simulation.

In order to compare Rg2 plots of a