Tuning interaction parameters of thermoplastic polyurethanes in a

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Tuning interaction parameters of thermoplastic polyurethanes in a binary solvent to achieve precise control over micro-phase separation Senem Merve Avaz Seven, Oguzhan Oguz, Yusuf Z. Menceloglu, and Canan Atilgan J. Chem. Inf. Model., Just Accepted Manuscript • DOI: 10.1021/acs.jcim.8b00781 • Publication Date (Web): 22 Feb 2019 Downloaded from http://pubs.acs.org on February 23, 2019

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Journal of Chemical Information and Modeling

Tuning interaction parameters of thermoplastic polyurethanes in a binary solvent to achieve precise control over micro-phase separation

Senem Avaz Seven1,3, Oguzhan Oguz2, Yusuf Ziya Menceloglu1,3,4, Canan Atilgan1,4* Sabanci University, Faculty of Engineering and Natural Sciences, 34956, Istanbul, Turkey École Polytechnique Fédérale de Lausanne (EPFL), Institute of Materials, Laboratory of Macromolecular and Organic Materials, 1015, Lausanne, Switzerland 3 Sabanci University Integrated Manufacturing Technologies Research and Application Center & Composite Technologies Center of Excellence, Teknopark, 34906 Pendik, Istanbul, Turkey 4 Sabanci University Nanotechnology Research and Application Center, SUNUM, 34956, Istanbul, Turkey * Correspondence: e-mail [email protected] 1

2

Abstract Thermoplastic polyurethanes (TPUs) are designed using a large variety of basic building blocks but are only synthesized in a limited number of solvent systems. Understanding the behavior of the copolymers in a selected solvent system is of particular interest to tune the intricate balance of microphase separation/mixing, which is the key mechanism behind the structure formation in TPUs. Here, we present a computationally efficient approach for selecting TPU building blocks and solvents based on their Flory–Huggins interaction parameters for a precise control over the micro-phase separation/mixing. We first cluster eight soft segments (PEO, PPO, PTMO, PBA, PCL, PDMS, PIB, or PEB) used frequently in TPUs into three categories according to the strength of their interactions with the binary solvent THF/DMF. We then perform a comprehensive set of dissipative particle dynamics simulations of the TPUs in a range of solvent ratios. This enables us to demonstrate the emergence of the unusual channel-like structures in a narrow range of parameters and to determine the critical interactions operative for obtaining either micro-phase separated or mixed structures. The findings are supported by thermodynamic arguments. The approach developed here is useful for designing novel TPUs with well-defined conformational characteristics, controlled morphologies, and advanced functional properties. 1. Introduction Thermoplastic polyurethanes (TPUs), i.e., segmented poly(urethane), poly(urea), and poly(urethane– urea) copolymers, are a broad and highly versatile class of polymers typically formed from an aromatic or aliphatic diisocyanate, a long–chain diol (or “oligo–polyol”), and a low molecular weight diol or diamine chain–extender, offering a practically unlimited range of structures along the multiple length scales that leads to an interesting combination of functional properties

1-4.

TPUs are designated by the

presence of urethane (–NHCO−O–) groups, although they may include other functional groups, such as ether, ester, urea or amide. Resulting materials can be considered as a segmented copolymer of macrodiol and diisocyanate–chain extender sequences, referred to as the soft segments (SS) and hard segments (HS), respectively.

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The most extensively used SS in TPU synthesis are poly(ethylene oxide) (PEO) oxide) (PPO)

12-15,

poly(tetramethylene oxide) (PTMO)

poly(caprolactone) (PCL)

22-24,

poly(ethylene butylene) (PEB)

16-19,

poly(dimethylsiloxane) (PDMS) 32

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5-13,

poly(propylene

poly(butylene adipate) (PBA) 25-30,

poly(isobutylene) (PIB)

31

20,21,

and

oligomers. The most distinct feature of the SS is a glass transition

temperature (Tg) well below ambient, rendering elastomeric characteristics of a TPU at service temperatures. HS, on the other hand, comprise strongly of hydrogen bonded urethane, urea and/or urethane–urea groups, which are formed by the reaction of diisocyanates with diol or diamine chain extenders and act as physical crosslinks with a dissociation temperature well beyond the service temperature range 3-5,7. The substantial number of commercially available starting materials with numerous compositional and structural features offer design flexibility, and thus, pave the way for the synthesis of TPUs with controlled morphologies and desired functional properties. However, this also means a multitude of critical design, synthesis and processing parameters4 that need to be controlled for both thermodynamic and kinetics related features of the matter. Considering their effects on micro–phase separation/mixing (thermodynamic control) and crystallization (kinetic control), some of the most important parameters, even in an oversimplified picture 4,5 may be listed as follows: (i) chemical composition, aromaticity, symmetry, size, length, size and length distribution, hydrogen bond strength and weight/volume fraction of the HS; (ii) chemical structure, end–group functionality, average chain length (molecular weight), polarity, solubility (typically characterized by Hildebrand solubility parameter), weight/volume fraction of the SS; (iii) thermodynamic incompatibility between HS and SS, nature and extent of intermolecular interactions (hydrogen bonding between HS–HS and/or HS–SS); (iv) polymerization procedure, reaction conditions and processing protocols. To date, many different experimental studies have been carried out to investigate effects of most of these parameters on the structure–property relationships of TPUs.

4,5,7,10,12-14,17,18,21,25,33,34

In many of

these studies, one of the parameters is considered as a single variable in a specific system. For instance, some of the studies have only reported the effect of hard segment weight/volume fraction

17,35-39,

whereas others have only focused on the effect of soft segment molecular weight. 7,14,33,40-45 The TPUs reported in such studies were usually synthesized in a particular solvent or in THF/DMF mixture.

46-51

However, most of these parameters also have combined effects on the structure–property relationships of TPUs, in addition to their individual effects. This increases the complexity of TPUs and requires more elaborated studies to be performed. Among the parameters related to reaction conditions and processing protocols, the selection of the solvent is critical for the preparation of TPUs 5,52,53 to be used for further investigation of their structure–property relationships in both solution and solid states. However, the number of studies focusing on this parameter is highly limited in the extensive base of


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TPU literature. 5,52-55 Moreover, introduction of dual solvents with different affinities to the SS and HS parts of TPUs bring about interesting new features to the behavior of the copolymers that are not obtainable by a single solvent

56.

In fact, tuning structure-property behavior of complex

macromolecules, such as copolymers, using dual solvent systems is a well-established approach encountered in the polymer physics literature. 56-59 Over the years, in line with the developments in computational tools 60, multi–scale modeling approach 60-65

has become of particular interest in numerous fields of science and technology where the

experimentally inaccessible information are predicted to gain insight into the physical mechanisms determining materials properties under various conditions. In this respect, complementary use of molecular dynamics (MD)

66-68

and dissipative particle dynamics (DPD)

69-71

simulations offers an

opportunity for a better understanding of the physical events taking place at different length scales that allows for the multi–scale characterization of complex materials from a bottom–up perspective, exemplified by our recent work. 62,72 In general, MD simulations on a polymeric system are preferably used to obtain atomistic details of molecular mechanisms for a single polymer chain. 5 This is mainly due to fact that MD simulations on a multi–chain system entail massive computational resources as they numerically solve Newton’s equation of motion for each atom in the system that also includes a large number of solvent molecules. 5

DPD simulations using coarse–grained representations where sets of atoms are clustered into beads

are therefore more favorable for multi–chain systems. 5 Accordingly, it is possible to describe physical mechanisms depending on the parameters critical for TPUs using MD and DPD simulation tools together. Nevertheless, the number of computational studies on TPUs is fairly limited as compared to that of experimental studies available in the literature. 5,63,73-84 Recently, Erekkath and Sreejalekshmi 74 presented theoretical predictions on tuning micro–phase separation with soft segment chain length and hard segment content to tailor shape memory effects in TPUs. Hu et al.

75

also studied shape memory

effects using DPD simulations for a series of TPUs with various hard segment contents. Zhu et al.

76

reported molecular simulation of TPUs under large tensile deformation. Yildirim et al. investigated effects of temperature 77, intersegmental interactions 78, symmetry and planarity of diisocyanate groups 79

on TPUs. Although these efforts provide valuable insights into the structure–property relationships

of TPUs, the following questions still remain to be addressed: (i) How does the pre–selected solvent system affects the physical mechanisms behind final morphology and properties? (ii) What is the role of soft segment chemical structure? (iii) Can these two parameters be evaluated as single variables independent to each other? If they cannot, (iv) what are their combined effects on the structure– property relationships of TPUs? To address these issues, here we mainly focus on the individual and combined effects of both solvent system and soft segment chemical structure on the conformational characteristics and final morphologies of a series of TPUs with the same HS composed of bis(4-isocyanatocyclohexyl)methane (HMDI) as the diisocyanate and 2-methyl-1,5-diaminopentane (MDAP) as the chain extender. Pure



tetrahydrofuran (THF), pure dimethylformamide (DMF) and binary THF/DMF mixtures with various molar fractions are chosen as the solvent set. Eight different SS chemical structures are evaluated for this selected HS and solvent pair. To give an exclusive focus on the effect of solvent ratio and SS identity, other significant parameters, such as HS/SS ratio and soft segment molecular weight, are also kept constant in addition to the HS chemical structure. Results obtained from the corresponding DPD simulations are discussed by means of density fields, radial distribution functions (RDFs), and segment molecular Gibbs free energy of mixing for quaternary systems. 2. Materials & Methods 2.1. Dataset We performed DPD simulations on a series of TPUs composed of various polyols as SS, selected from amongst the most widely used polyols in TPU synthesis as explained previously.4 Figure 1-a demonstrates the topology of the TPUs constructed for DPD simulations. While changing the SS oligomers, HS chemistry (HMDI+MDAP) is kept fixed. SS groups are selected from the monomeric units of PEO, PPO, PTMO, PBA, PCL, PDMS, PIB, or PEB. Each SS bead is composed of one monomeric unit of corresponding SS polymers, except PEO and PBA. To conform to the FloryHuggins theory, DPD parameterization requires all the beads to be in equal or comparable molecular volumes

85,86.

To satisfy this requirement, PEO beads are set to contain two monomeric units of

ethylene oxide (1,2-dimoethoxyethane). Meanwhile PBA beads contain partial monomeric units, such as propyl acetate and methyl butanoate; thus, PBA-1 and PBA-2 represent two different possibilities of the PBA monomer (Figure 1-b). To map the monomeric units of the polymer into beads, coarse graining for each TPU copolymer was carried out as follows: HS was partitioned into A, B and C type of beads corresponding to urethane/urea, methylcyclohexane and MDAP, respectively (Figure 1-c). Each SS was coarse-grained into beads in a range of molecular weight between 90.1 and 118.2 a.m.u. In this respect, PEO beads correspond to two repeating units of ethylene oxide, while the rest of the SS set correspond to one repeating unit per bead. The chemical structures of the SS beads are shown in Figure 1-b. PBA beads were constructed for two different alternatives, both representing one repeating unit labelled PBA-1 or PBA-2.

2.2 DPD Parameterization Once the coarse graining was completed, cohesive energy densities (CED), Flory-Huggins interaction parameters (𝜒𝑖𝑗), and DPD parameters (𝛼𝑖𝑗) between SS and solvent beads were computed by performing short MD simulations as explained in detail in our previous study 5; see Supporting Information for equations 1-3 leading to the DPD parameters and the individual values needed for this calculation. As a reminder, in this parameterization, 𝛼𝑖𝑗 = 25 corresponds to neutral (self) interactions,


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while repulsions get stronger as the DPD values grow larger. To calculate CED and 𝜒𝑖𝑗 for each bead, at least three short MD simulations, composed of 1 ps equilibration and consecutive 100 ps were performed in the NVT ensemble on simulation boxes composed of 10 beads

87.

To check the

convergence of these parameters, simulations necessary for the PEB-DMF interaction were repeated for boxes containing 20 and 100 beads, and for simulation lengths of 100 and 200 ps; the error margin in the final DPD parameter is confirmed to be ±0.1 DPD units (Supporting Information, Table S-3). During all the simulations, densities are kept as 1.0 g/cc for copolymer beads and density values of 0.89 and 0.94 g/cc were fixed for THF and DMF simulations, respectively. Simulation boxes were obtained by Amorphous Cell construction tool

88

of Materials Studio 6.0

89.

NVT ensembles were

obtained by the FORCITE package, using COMPASS27 (Condensed-phase Optimized Molecular Potentials for Atomistic Simulation Studies) Forcefield

90.

MD Simulations were carried out in pure

solvents of THF and DMF, and 𝛼𝑖𝑗 were calculated according to

70.

Calculated 𝛼𝑖𝑗 values against

solvents are plotted comparatively in Figure 2. It is important to note that no significant difference was observed between DPD parameters of PBA1 and PBA2 in either solvent. Therefore, this soft segment will be represented as PBA henceforth.

Soft Segment

Hard Segment

a

Chain Extender

b

c

Bead A PEO

PPO

PBA-1

PTMO

PBA-2 Bead B

PCL

PDMS

PIB

PEB

Bead C

Figure 1 (a) Schematic diagram demonstrating the copolymer; (b) 3D chemical structures of soft segments, (c) hard segment bead types used in the study. Polymerization ends of the building blocks are marked with stars.



3

2

1

Figure 2 Comparison of DPD parameters of SS in pure THF vs. DMF. Groups determined regarding the DPD interaction parameters separate into three regions in the DMF/THF parameter space.

The comparison leads to grouping the SS into three categories according to how they separate into regions in the DMF/THF parameter space of Figure 2, highlighted in green, yellow and red, respectively: The first group, composed of PEO, PPO, PBA and PCL, points to nearly neutral interactions between SS and THF (ij = 25.04±0.01), and repulsive towards DMF (ij = 29.5±0.3), considering that the neutral interaction is 25.0. In the second group of PTMO and PDMS, SS displays moderate interactions with THF (26.0±0.3) and are strongly repulsive towards DMF (32.80±0.74). In the third group, the average DPD parameters of SS composed of PIB and PEB are repulsive for THF (27.97±0.34) and very strongly repulsive towards DMF (39.08±1.28). Notice that DMF is always a poorer solvent than THF for the SS. We select a representative SS chain from each group and perform DPD simulations on these distinct groups. Further calculations were thus carried out on TPU structures having PEO-like, PTMO-like and PEB-like as SS (labelled PEO-TPU, PTMO-TPU and PEB-TPU, respectively). Table 1 lists the calculated Flory-Huggins interaction (𝜒𝑖𝑗), and DPD (𝛼𝑖𝑗) parameters for group representatives; the A, B, C bead types are displayed explicitly in Table 2. The numbers of beads are described in detail in section 2.3.


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Page 7 of 21

1 2 3

𝝌𝒊𝒋 or 𝛼𝑖𝑗

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 1 Calculated Flory-Huggins interaction (𝜒𝑖𝑗), and DPD (𝛼𝑖𝑗) parameters of the soft segments. In each table, values in the lower diagonal represent 𝜒𝑖𝑗 while those in the upper diagonal represent 𝛼𝑖𝑗 parameters (bold). Values relevant to the differing SS bead groups are in shaded cells.

A B C PEO/PTMO/PEB THF DMF

4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

A 25. 3.17 0.63 0.23/3.97/6.44 2.13 0.41

B 35.4 25. 1.64 2.10/0.20/0.84 0.01 1.32

Bead Type C 27.1 30.1 25. 0.09/2.69/4.77 1.13 0.00

PEO/PTMO/PEB 25.7/38.0/46.1 31.9/25.6/27.7 25.3/33.8/40.6 25. 1.50/0.21/0.80 0.05/2.18/3.91

THF 32.0 25.0 28.7 25.2/25.7/27.6 25. 0.86

2.3. DPD Simulations in Solvent Mixture To investigate the effect of dual solvent mixture on the copolymer’s conformation and morphology, we carried out a set of DPD simulations on TPU copolymers. The solvent set was composed of pure THF, pure DMF and mixtures of THF/DMF at varying mole fractions. TPU copolymer chain was constructed using 46 repeating units of SS and 18 units of HS partitioned as 8 A, 8 B and 2 C beads. DPD simulations were carried out for solutions containing 10% copolymer in the solvent mixture. Bead chemistries and the number of beads used in each DPD simulation are shown in Table 2. Note that the numbers of solvent particles are kept fixed while their fractions are varied in a series of DPD simulations. Mesoscale simulations were performed using DPD tool of Materials Studio 6.0 Package

89.

DPD

simulations were performed in two stages. In the first stage, 20000 steps DPD simulations were performed to reach equilibration. In the second stage, 50000 steps of production DPD runs were performed to obtain the trajectories used in the analyses. All DPD simulations were performed in a box with a fixed density of 3 DPD units, a spring constant of 4.0, while the temperature was set to unity. Table 2 Structure and the number of beads used in DPD simulations.

A

B

Bead Chemistry C SS

A 80 80 80

B 80 80 80

Number of Beads C SS 20 460 20 460 20 460

THF

DMF

PEO-TPU PTMO-TPU PEB-TPU

22

DMF 26.3 29.3 25.0 29.9/32.1/37.8 28.0 25.

PEO-TPU PTMO-TPU PEB-TPU


Solvent 5760 5760 5760


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37

3. Results The SS morphologies of PEO-TPU (purple), PTMO-TPU (cyan) and PEB-TPU (magenta) obtained by the end of 50000 steps of DPD simulations are displayed in Figure 3-a. One observes three phases of SS in each TPU structure. In one morphology there is phase separation where SS beads are organized to form segregated clusters, as exemplified by PEB-TPU in pure DMF (Figure 3-a, magenta). In another set of morphologies, there is channel-like formation

91-93

whereby SS beads are partially

integrated into the HS (shown as lines around density fields for simpler representation); e.g. in PTMOTPU (Figure 3-a cyan, 0.5 THF fraction). In the final set, there is phase mixing of SS into HS (all systems in pure THF); e.g. in PEO-TPU, a transition from channel-like formations to phase mixed states is clearly obtained as THF content in the solvent is increased. In fact, in all cases, there is a micro-phase change from phase separation to channel formation to phase mixing as the THF content increases. This is mainly because polymer-THF interactions are always stronger than polymer-DMF interactions as THF is a better solvent than DMF for all the copolymers investigated. Therefore, they obey the same physical driving forces throughout the structure formation, resulting in the morphological switch between the phase mixing and separation, regardless of the SS chemical structure, which is no longer a dominant factor as soon as the soft segment is unable to preserve its most favorable conformation. Note that channel-like structures in PEB-TPU are observed after 0.7 THF fractions. Since our TPU simulation dataset contains 0.0, 0.3, 0.5, 0.7 and 1.0 THF fractions only, we could not demonstrate the channels explicitly for this copolymer. More detailed information on channel-like formations in PEB-TPU at 0.85 THF fraction is found on Supporting Information Figure S-3. The increase in THF amount in the solvent is quantified by the increase in the radii of gyration (Rg) calculated from the DPD trajectories (Figure 3-b). The increase in Rg is consistent with the fact that the DPD interaction parameters for SS in DMF are always more repulsive than those for SS in THF (Figure 2). Thus, as the overall repulsions towards the SS beads decrease, they occupy a larger volume in the mixture. Interestingly, the rate of increase in Rg is not dependent on the phase, but on the SS categories encircled in Figure 2. In other words, morphology changes are observed during dual solvent exchange within every SS category, while the conformational preference of individual chains is governed by DPD parameters. Further analyses were carried out to reveal the driving forces behind these morphological and conformational changes with varying THF:DMF solvent ratio. To investigate the structural changes behind phase separation to mixing dynamics of segments, we focused on self- and inter-segmental interactions of TPUs, as well as their interactions with the dual solvent.


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a

b

PEB46-TPU PTMO46-TPU PEO46-TPU

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.0

0.3

0.5

0.7

1.0

THF Fraction

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

Figure 3 Density fields of SS obtained from DPD trajectories (a) of PEO-TPU (top), PTMO-TPU (middle) and PEB-TPU (bottom). SS density fields of PEO-TPU, PTMO-TPU and PEB-TPU are represented in purple, cyan and magenta, respectively. Solvent beads are turned off, and HS beads are in line representation for better visualization. The white regions represent cross-section profiles of density fields where 2x2x2 expansion of periodic images intersects the density field. In HS, A, B, and C beads are shown in red, green and blue, respectively. Radii of gyration (b) of PEO-TPU (black), PTMO-TPU (blue) and PEB-TPU (magenta) with respect to THF fraction. DPD trajectories of phase separation (PTMO, THF 0.15), channel-like formations (PTMO, THF 0.30) and phase mixing (PTMO, TF0.80) are also included as Web Enhanced Object (WEO) and attached to the html version of this manuscript.

We first investigate SS-SS interactions in varying THF:DMF ratios via the RDFs as displayed in Figure 4-a. As the concentration of THF in the solvent mixture is decreased, the SS self-interactions increasingly dominate the distribution of the beads. The origin of micro phase separation is clearly demonstrated to be the local SS-SS interactions, as exemplified in pure DMF in Figure 4-b. As THF co-solvent is added to the system, self-interactions of SS diminish, and inter-bead interactions are favored against SS-SS interactions. This way, packed SS chains start to disentangle (Figure 4-c) until they are phase mixed (Figure 4-d). This result confirms our previous finding in which a similar trend is observed in RDFs of PEO based TPUs.5 Note that the RDFs obtained for the copolymer shown in Figure 4 is a representative of all systems studied. Detailed analysis on SS self-interactions of PEOTPU, PTMO-TPU and PEB-TPU are given in Supporting Information Figure S-1. a

Phase Separation

b d

22 23 24 25

Channel Formation

c

Phase mixing

d

Figure 4 (a) RDFs between SS beads of the PTMO-TPU copolymer at different solvent ratios. RDFs obtained for this copolymer is representative of all systems studied. Copolymers-pure solvents RDFs are shown in bold lines. (b-d) Representative conformations of multiple chains of PTMO-TPU obtained from the final DPD snapshots at



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

the THF fractions of 0, 0.5, and 1, respectively. Here, SS (magenta), A (blue), B (green) and C (red) beads of the copolymer are displayed and solvent molecules are turned off.

The SS-solvent interactions provide part of the story in understanding the overall morphologies of these systems. Another important component that affects morphological traits is intersegmental interactions established between HS and SS beads (Figure 5). Plotting RDFs between SS and HS beads, we observe that the probability of finding A and B type of HS beads near SS beads depends on solvent ratio (Figure 5-a-c), while C type of beads are independent of the content of the solvent mixture (not displayed). For this reason, RDFs of C type beads are not discussed further. While there are equal numbers of A and B beads in all systems (Table 2), B beads are statistically more prominent near the SS beads than A beads in phase separated morphologies (Figure 4-a). During channel formation, the SS-A and SS-B interactions are equally likely, contributing synergistically to channel formation (Figure 4-b). As the conformation of SS starts to extend, SS-A interactions slightly dominate SS-B (Figure 4-c). Thus, a conformational switch takes place between A and B beads during the transition from phase separation (Figure 4-d) to phase mixing (Figure 4-e) of segments. Details of RDF analysis on SS-HS of PEO-TPU, PTMO-TPU and PEB-TPU are given in Supporting Figure S-2. While the compact and fully extended conformations of single chains of phase separated and phase mixed structures are stable and give an idea about the meso-scale structures they are involved in, for the case of channel-like structure forming chains, there is a wide distribution of conformations. Sample conformers for each system are also displayed in figure 5 as insets.

a

22 23 24 25 26 27 28 29 30 31 32 33 34

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Phase Separation

c

b

Channel Formation

Phase Mixing

Figure 5 RDFs of PTMO-TPU SS beads plotted against A (___) and B (_ _ _) types of beads of HS for phaseseparated (a), channel-formed (b) and phase-mixed (c) structures. Molecular conformations of (a), (b) and (c) are given as insets. 3D molecular structures of TPUs in corresponding solvent ratios are given in line representation; SS (pink), A (blue), B (green) and C (red).

We finally monitor solvent – SS interactions in detail. We first note that the SS-DMF interactions are always weaker than SS-THF interactions, independent of solvent ratio (Figure 6). This is in line with the fact that THF is a better solvent than DMF for our copolymers, which are dominated by SS beads (Figure 2). In pure DMF, the number densities of DMF beads close to the SS beads are small and therefore DMF cannot solvate SS chains, resulting in packed SS copolymer conformations (Figure 6, black dashed line). As the cosolvent THF is added to the system, SS-DMF interactions become more favorable at short range (Figure 6-a, dashed lines) and copolymer chains expand, leading to phase mixing. Interestingly, the probability of THF molecules to be found in the solvation shell is highest in


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1 2 3 4 5 6 7 8

the smallest THF fraction (Figure 6-a, solid lines). As a good solvent, THF easily penetrates into the solvation shell of the copolymer, giving rise to a change in its conformation from packed to extended. As THF penetrates and copolymer coils extend, solvent interaction sites on the copolymer become increasingly available to both solvents. This creates the unusual case where SS-DMF interactions become more favorable in THF/DMF mixtures than pure DMF. Note that there is a gap between SSTHF and SS-DMF interactions in every solvent mixture. This gap shrinks as we reach higher THF concentrations. In other words, as the probability of THF and DMF beads to be in the solvation shell gets more similar, the copolymer extends, and phase mixing is observed. Phase Separation

b

a

0.2 THF Channel Formation

c

0.4 THF Phase Mixing

d

0.8 THF

9 10 11 12 13 14 15 16

Figure 6 RDFs of PTMO-TPU SS beads plotted against solvent beads at different THF:DMF ratio (a). In each solvent ratio, SS-THF interactions are represented by solid lines while SS-DMF interactions are represented by dashed lines. SS-solvent interactions in pure THF and pure DMF are represented in bold black and grey lines, respectively. RDFs obtained with other copolymers are similar to PTMO-TPU; therefore they are not given here. 3D molecular structures of TPUS in corresponding solvent ratios are given in line representation (b, c, d). Pink, blue, green and red beads represent SS, A, B and C type of beads, respectively. Solvents THF and DMF are represented in dot form, in cyan and red, respectively.

17 18 19 20 21 22 23 24 25 26 27

While the solvent beads, with their high mobility and interplay between the range of interactions contribute to the chain conformations (Figure 6), the role of HS beads (bead types A and B) are also important. The effective HS-SS interactions display a switching as the phases change (Figure 5). In Figure 7, we overlay the solvent-HS RDFs on those displayed in Figure 5 to get a better overall picture of the quaternary system. In the packed conformation, exemplified by the PTMO-TPU in pure DMF system (Figure 7-a), there is a layered structure. In the innermost layer are the SS beads collapsed to form a globular structure; these are predominantly surrounded by B type beads while A beads occupy a slightly more distant position. We note that while the SS-A interactions are highly unfavorable for this system (Table 2), chain connectivity allows this positioning for the A beads. At the outermost layer are the solvent beads which have a much lower chance to penetrate near the region populated by the SS,



1 2 3 4 5 6 7 8 9 10 11 12

despite their high mobility. Their higher affinity towards A-type beads over B-type reflects only slightly in the overall RDF. As enough of the cosolvent (THF) is introduced to the system (Figure 7-b), the conformation of the copolymer switches to extended form, while solvent beads are able to displace HS and interact directly with SS. This results in somewhat enhanced A-DMF interactions (Figure 7-b, pink dashed line). Barring minor changes due to the positioning of the beads on the copolymer, the rest of the bead distributions are rather “egalitarian” in the channel formed systems. Therefore, we conclude that ADMF interactions are the primary cause sustaining the channel formation. This delicate balance is offset when more THF is added to the system where the copolymer is fully extended to form the mixed phase in pure THF (Figure 7-c). At this extreme, the probabilities of THF beads to come in close contact with HS get equally probable to SS-A, diminishing SS-B interactions. a

13 14 15 16 17 18 19

Page 12 of 21

b

Phase Separation

c

Channel Formation

Phase Mixing

Figure 7 RDFs of PTMO-TPU copolymer SS beads plotted against A (black line), B (red line), THF (solid line) and DMF (dashed line) beads. (a) HS-solvent interactions in pure DMF (phase separation; (b) 0.5 THF (channel formation; (c) pure THF (phase mixing). In each solvent ratio, SS-HS interactions are represented by solid lines while SS-Solvent interactions are represented by dashed lines. RDFs obtained for the other copolymers have similar trends (not displayed).

20 21

4. Discussion

22 23 24

We generalize the segment molar Gibbs free energy of mixing, defined originally for binary systems composed of either polymer/solvent or polymer/polymer mixtures systems

95

and later extended to ternary

as, ∆𝐺 𝑅𝑇

25 26 27 28 29 30 31 32 33

94,

𝑁

1

𝑁

𝑁

= ∑𝑖 = 1𝑁𝑖𝜑𝑖𝑙𝑛𝜑𝑖 + ∑𝑖 = 1∑𝑗 = 𝑖 + 1𝑔𝑖𝑗𝜑𝑖𝜑𝑗

(1)

where 𝜑𝑖 is the volume fraction and Ni is the number of segments of each component. The first term on the right-hand-side of the equation is the purely entropic combinatorial part. The double summation is called the integral Flory Huggins interaction parameter, a residual part that is experimentally inaccessible and chemical potential dependent. Wolf

96,97

and Stryuk

98

define the last term as the sum of two effects; one that takes into account

breaking of local contacts due to the insertion of solvent beads and another that is related to the conformational relaxations once the insertion takes place. Due to the assumptions inherent to DPD


Page 13 of 21 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1 2

simulations, particularly the requirement of selecting beads of similar volume, the expression for the

3

𝑔𝑖𝑗 = (1 ― 𝜈𝑖𝑗)(1 ― 𝜈𝑖𝑗𝜑𝑗(1 ― 𝜑𝑘)(1 ― 𝜑𝑙)) ― 𝜁𝑖𝑗(1 + 2𝜑𝑗(1 ― 𝜑𝑘)(1 ― 𝜑𝑙))

4 5 6

The first term is characterized by two parameters, αij that is related to contact breaking and ij for the

𝑔𝑖𝑗 term simplifies to, 𝛼𝑖𝑗

1

deviation of entropy from combinatorial behavior

97,98.

(2)

The conformational relaxation of the polymer

during mixing is symbolized by ζij which approaches zero in theta solvent conditions; this term will

7 8 9 10 11 12 13 14 15

only exist between polymer-solvent bead types 99. αij is calculated via the relationship (2ij-E)/[2(1-E)]

16 17 18 19 20

fraction of THF in the solvent mixture, 𝜑𝑇𝐻𝐹/(𝜑𝑇𝐻𝐹 + 𝜑𝐷𝑀𝐹). The result for the three types of systems

21 22 23 24 25 26 27 28 29

where E is a constant specific for a given class of polymers (0.7 is a usual choice for vinyl polymers). Similarly, ij is calculated via [E(2ij-1)/(1-E)]. Noting that increasing ij reduces solvent quality, we examine the RDF curves to set it to 0.05 for HS-DMF and SS-THF pairs; and to 0.5 for HS-THF and SS-DMF pairs. For the DMF-THF interactions, we take ij = 0.7. We use the ij values listed in Table 1. We may thus plot the phase diagrams for our systems which, due to Table 2, have 𝜑𝐻𝑆= 180/6400 and have 𝜑𝑆𝑆= 460/6400 in all our simulations. We may thus monitor the phase behavior along the relative studied in this work is displayed in Figure 8. Note that there is an extra entropic loss due to constraining the HS and SS beads into a single chain; however, since we keep the number and length of the polymer chains fixed, this will bring in an additive constant to all curves.

Figure 8 Phase diagrams of PEO-TPU (purple), PTMO-TPU (cyan), and PEB-TPU (magenta) systems constructed using segment molar Gibbs free energy of mixing for quaternary systems.

With this choice of parameters, the systems have two minima at THF rich and DMF rich ends. At low THF fractions in the quaternary system, we find the systems we have hitherto labelled “phase separation” whereby the spherical polymeric precipitates are surrounded by the nearly pure DMF molecules, whereas the little amount of existing THF molecules are predominantly accepted in between the polymeric chains, as indicated by the RDFs in Figure 6a. At high THF fractions, we find the phase



1 2 3 4 5 6 7

mixed systems where not only are the chains at their largest Rg values (Figure 3-b), but also the THF

8

5. Conclusions

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39

and DMF molecules are at closest contact distance with each other (Figure 6-a). In the region of metastability between the inflection points of the curves, the microstructure sets out to satisfy two conditions at once, with the THF beads staying near the chains in close proximity to the channel-like structures and the DMF rich regions permeating the region between the channels. The symmetry in the curve determines the extent to which the channel-like structures will be discernible.

We have studied the effect of solvent ratio on the morphology of TPU copolymers for a range of SS chemistries using DPD simulations. During DPD parameterization, we have classified the SS into three groups with respect to their interactions with the solvents employed in the study. We have then performed DPD simulations on three TPU copolymers, each representing one group of SS. Independent of SS chemistry, DPD simulations displayed three different morphologies for the system. These are, (i) complete separation of HS and SS phases, (ii) formation of channel-like structures in SS, and (iii) mixing of HS and SS phases. After performing a set of DPD simulations on copolymers at varying THF:DMF solvent ratios, we observe that the morphologies are dependent on solvent ratio. Copolymers are phase-separated in pure DMF and in low concentrations of THF. As the THF ratio increases, the copolymer starts to expand, forming the intermediate phase containing channels, and finally phase-mixing occurs at higher THF concentrations and pure THF. From the viewpoint of the copolymer, a compact SS conformation is observed in phase separation, where SS-SS interactions dominate over SS-HS and SS-solvent interactions. As the copolymers disentangle giving rise to channel formation and phase mixing, SS-SS interactions become less favorable. With respect to inter-segmental interactions in the copolymers, SS-B interactions are more dominant in phase-separated structures. The probabilities of A and B beads to be found near SS become comparable in channel-like structure formation. Finally, SS-A interactions dominate over SS-B in the phase-mixed structures. We thus conclude that as the polymer extends, HS conformations switch so that SS-A type of interactions become more favorable while B type beads establish closer contact with solvent molecules. From the viewpoint of the solvent, copolymer inter-segmental interactions are significantly more favorable in the phase-separated structure, but SS-solvent and HS-solvent interactions grow as the copolymer conformations switch to phase mixing due to chain extension. During channel formation, THF comes into closer contact with SS beads and solvates them, while DMF approaches to HS beads, particularly to the A type. Therefore, we conclude that THF beads help expand the copolymer structure, while DMF beads contribute to the stabilization of the expanded structure. Combining these results with our previous finding that SS-A interactions, namely SS-urethane, giving rise to channellike structure formation, we find that SS-A interactions are the main driving force behind phase transition of TPU copolymers, supported by the dual solvent system in which SS are found close to


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

THF, and HS to DMF. Furthermore, as shown in Figure 6, SS-DMF interactions are always weaker

31

References

32 33 34 35 36 37 38 39 40 41 42 43

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than SS-THF interactions, independent of solvent ratio, in line with the fact that THF is a better solvent than DMF for all our SS. Thus, as a good solvent, THF easily penetrates into the solvation shell of the copolymer, leading to a conformational change from packed to extended state that renders SS-DMF interactions more favorable. To support these findings, we have expanded the integral Flory interaction parameter theory to quaternary systems in this study. We have demonstrated that DPD simulations are particularly suitable for predicting the parameters of the theory. Our results enhance the understanding on the conformational states of segmented TPU copolymers and offers strategies to tune their morphology using complex solvent systems at different ratios. As a future direction, we plan to generalize the construction of the phase diagrams of quaternary systems based-on the findings of the current study. Acknowledgements. This work was supported by the Scientific and Technological Research Council of Turkey (Grant Number 117F389). We thank Dr. Ali Rana Atilgan for many stimulating discussions. Supporting Information (SI): Table S-1: Molecular weights, calculated Cohesive Energy Densities (CED), Solubility Parameters and molar volumes of beads employed. Table S-2: Average molar volumes, Square differences of solubility parameters, Interaction parameters and DPD parameters for each bead pair employed. Table S-3: PEB-DMF interaction parameters repeated for boxes containing 20 and 100 beads, and for simulation lengths of 200 and 500 ps and error margins. Figure S-1: RDFs of SS beads and 3D structures of the copolymers at different solvent ratios. Figure S-2: RDFs of SS beads plotted against HS and molecular conformations of copolymers Figure S-3: PEB-DMF interaction parameters and error margins from repeated runs with boxes containing 20 and 100 beads, and for simulation lengths of 100 and 200 ps. This information is available free of charge via the Internet at http://pubs.acs.org Conflict of Interest: Authors declare that that there is no conflict of interest regarding the publication of this article.



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Table of Contents

1

TPUs Hard Segment

2

Micro-phase Separation

Soft Segment

Channel Formation


Micro-phase Mixing

THF DMF HS SS

Tuning interaction parameters of thermoplastic polyurethanes in a

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