Computer simulation of thermoplastic elastomers from rubber-plastic blends and comparison with experiments

Computer simulation of thermoplastic elastomers from rubber-plastic blends and comparison with experiments

Accepted Manuscript Computer simulation of thermoplastic elastomers from rubber-plastic blends and comparison with experiments Subhabrata Saha, Anil K...

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Accepted Manuscript Computer simulation of thermoplastic elastomers from rubber-plastic blends and comparison with experiments Subhabrata Saha, Anil K. Bhowmick PII:

S0032-3861(16)30856-4

DOI:

10.1016/j.polymer.2016.09.065

Reference:

JPOL 19071

To appear in:

Polymer

Received Date: 26 June 2016 Revised Date:

15 September 2016

Accepted Date: 18 September 2016

Please cite this article as: Saha S, Bhowmick AK, Computer simulation of thermoplastic elastomers from rubber-plastic blends and comparison with experiments, Polymer (2016), doi: 10.1016/ j.polymer.2016.09.065. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Simulation

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Experiment

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Computer simulation of thermoplastic elastomers from rubber-plastic blends and comparison with experiments Subhabrata Saha, Anil K Bhowmick* Rubber Technology Centre, Indian Institute of Technology, Kharagpur 721 302, India Telephone: 91-3222-283180; *Fax: 91-3222-220312;

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*

*Email: [email protected] & [email protected]

ABSTRACT:

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Computer simulation could be a useful technique to scrutinize the properties of individual polymers as well as their blends. However, there is no work on computer simulation of thermoplastic elastomer from rubber-plastic blends. As representative example, binary

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compatibility of polyamide 6 (PA6) with fluoroelastomer (FKM) for a 40/60 composition of PA6/FKM thermoplastic elastomer was investigated by atomistic simulation and mesoscale dissipative particle dynamics simulation. The specific volume of PA6, FKM and their blend was studied at various temperatures to estimate the glass-rubber transition. The glass transition temperatures of pristine PA6 and FKM were found to be 336K and 250K respectively in line with the experimental values. The blend system displayed two distinct

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glass transition temperatures (348K and 254K for PA6 40FKM 60) as discerned from atomistic simulation. These values were also in agreement with the experimental findings. Two Tgs described immiscibility in the present composition. The Flory-Huggins interaction parameter χ, as determined from atomistic simulation, was

estimated to be 0.25, also

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consistent with the experimental result. Among different potential energy contributions, van der Waals energy and torsion energy showed distinct inflection points for both the pristine polymers and their blend. These inflection points were near the glass transition temperature

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of the respective polymers. Polymer chain mobility depicted from the mean square displacement emphasized faster relaxation of PA6 over FKM in the blend. Dissipative particle dynamics (mesoscale) simulation suggested phase separation and dispersion of FKM in the PA6 matrix in line with the experimental results.

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1. INTRODUCTION: Thermoplastic elastomers are advance materials which behave like a rubber at ambient temperature, but have the processing ability like plastics [1]. In thermoplastic

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elastomers from rubber-plastic blends, both the rubber domains and the resinous thermoplastic domains co-exist [2]. They display adequate combination of mechanical properties and low temperature flexibilities along with the ease of processability like

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thermoplastics such as extrusion and injection moulding as well as recycling abilities [3]. Blending of a rubber with thermodynamically miscible thermoplastic gives monophasic

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morphology with a single glass transition temperature and often shows highly damped, almost leather like characteristics. Heterophasic morphology where soft rubbery domains are loosely bonded (if at all) with hard thermoplastic domains can only be obtained if the constituent polymers are thermodynamically immiscible [4]. The low glass transition temperature would be maintained because of the rubber phase, while high glass transition

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temperature of thermoplastic could help in mechanical integrity. Knowledge of microscopic morphology of the blends is important for predicting the macroscopic properties. Enthalpy of mixing, glass transition temperature, dynamic mechanical properties, scanning electron

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microscopy, transmission electron microscopy, atomic force microscopy etc. have been

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utilized extensively for understanding the morphology of these blends [5,6]. Several researchers have designed thermoplastic elastomers from different rubber-

plastic blends and studied their properties [7-9]. Banerjee and Bhowmick have enlightened the development of morphology of a new thermoplastic elastomer, based on PA6 and FKM, with time during dynamic vulcanization [10]. Rheological properties like shear viscosity, shear modulus, die swell, extrudate surface have been monitored for numerous thermoplastic elastomeric systems over the years [11,12]. Banerjee et al. have assessed the interaction parameter of PA6/FKM blends through rheological measurement by estimating the interfacial 2|Page

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tension between the dispersed rubber phase and the continuous matrix of thermoplastic [13]. Jha and Bhowmick have proposed degradation mechanism for thermoplastic elastomeric blend of PA6/acrylate rubber and showed the alteration in tensile properties with aging time

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[14], whereas, Herrera et al. have examined the volatile substances liberated during thermal degradation of thermoplastic polyurethane [15]. Lin et al. have looked into strain dependent resistivity of thermoplastic polyurethane filled with carbon filler and functionalized carbon

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nanotube [16]. However, understanding of these systems from theoretical aspect is still obscure.

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Recent advancement in computational technique creates a revolutionary change in predicting the miscibility and phase behaviour of the polymeric blend system with the help of molecular dynamics (MD) simulation. Molecular dynamics connect the microscopic properties and macroscopic properties via statistical mechanics based on mathematical expressions. Fan et al. have shown a systematic approach to determine the temperature

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dependence of Flory-Huggins interaction parameter for the binary mixture of solvent-solvent, solvent–polymer and polymer-polymer by using Monte Carlo method of polymer sampling [17]. However, accuracy in the calculation of polymeric binary mixture depends on the

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theoretical model and force field type. Tiller and Gorella have developed a new algorithm for molecular mechanics calculation in order to calculate the enthalpy of mixing of a pair of

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polymer segments and compared the results with the existing amorphous cell module [18]. Amorphous cell module was found to be more detailed, while new algorithm was convenient to preliminary screening of potential blends. Choi et al. have estimated the equation of state parameters for polystyrene and poly(vinyl methyl ether) from molecular simulation [19]. Atomistic simulation was also utilized to study the interfaces of polyamide-6,6/carbon nanotube nanocomposite by Eslami et al. [20]. In contrast, dissipative particle dynamics (DPD) method could extend the length and time scale by several order of magnitude as 3|Page

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compared to atomistic simulation [21,22]. In DPD method, atoms are grouped together up to the characteristic length of the polymer chain. Jawalkar et al. have studied the kinetic phase separation via density profile calculation using mesoscopic simulation technique for the

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incompatible blend of polyvinyl alcohol and polymethyl methacrylate [23]. Gai et al. have utilized the DPD simulation method to understand the phase morphology of ultrahigh molecular weight polyethylene/polypropylene/polyethylene glycol [24].The effect of volume

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fraction and shear rate was discussed in details by the authors.

Polyamides are engineering thermoplastics having great importance in recent years

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because of its high strength, stiffness, thermal resistance, wear resistance and low friction, whereas fluoroelastomer (FKM) provides excellent chemical and thermal resistance. Eslami et al. have studied the structure, dynamics and rheological properties of polyamide-6,6 from atomistic simulation as well as coarse grain simulation [25-29]. However, thermoplastic elastomeric blends from polyamide 6 and FKM were not studied so far by atomistic and

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mesoscale simulations. In the present study, detailed atomistic simulation was conducted for the thermoplastic elastomeric blend of PA6/FKM for the first time and compared with the experimental results. Compatibility between the two components was evaluated in two ways.

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First glass transition temperatures were measured from specific volume vs temperature plot for the pure polymers followed by the blend system. Further, this result was confirmed by

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Flory-Huggins interaction parameter calculated from cohesive energy densities at room temperature. We also attempted to understand the fundamental atomic level interactions; different energy components were studied against temperature to predict the contribution of the components towards the glass transition. We have also tried to explore the dynamics of polymer chains in pristine and in the blend system. Finally, DPD simulation was carried out for predicting the morphology. All findings were compared with the experimental results.

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2. SIMULATION METHODS: 2.1 Molecular Dynamics (MD) Simulations:

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MD simulations were performed to study the PA6/FKM blends using Dassault Systèmes BIOVIA Material Studio software (version 16.1.0.21). Homopolymer of PA6 and FKM was first constructed containing 30 and 40 repeat units for PA6 and FKM respectively with Materials Visualizer within the Material Studio. For each composition, a cubic

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simulation box was designed based on the packing theory proposed by Theodorou and Suter [30] using Amorphous Cell module. The weight fractions of the blends including the

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homopolymers, the total number of chains and repeat units, initial densities and box dimensions are listed in Table 1. A number of configurations were constructed for each composition and each of which was subjected to energy minimization by the ab initio Condensed-phase Optimized Molecular Potentials for Atomistic Simulation Studies

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(COMPASS) force field [23]. The total potential energy is expressed as follows: ET= Ebond + Enonbond + Ecross (1)

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= Eb + Eθ +Eφ+ Evdw + Ecoulomb + Ecross

where Eb is bond stretching energy, Eθ is angle bending energy and Eφ is dihedral torsion

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energy and all three together are expressed as a bonded energy or Ebond. Non-bonded energy Enonbond is the combination of van der Waals energy Evdw and columbic energy Ecoulomb. Ecross is the energy of cross terms between any two of the bonded items, such as the bond-angle cross term and the bond-bond cross term.

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Table 1 Input parameters for cubic simulation boxes for pristine PA6, FKM and their blend.

Number

Total number

Initial density

Cell dimension

designation

of chain

of repeat units

(g/cc)

(Å)

PA6

5

150

1.14

33.73

FKM

5

200

1.82

26.58

PA6 40FKM 60

2 PA6/ 2

140

1.47

33.05

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FKM

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Sample

All initial configurations from each composition were subjected to 5000 steps energy

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minimization using Forcite module with energy convergence threshold of 0.001 kcal/mol and force convergence of 0.5 kcal/mol/Å. The Ewald summation method was applied for electrostatic interaction with accuracy level of 0.001 kcal/mol and the Atom based summation was adopted for van der Waals interactions. Minimum energy configurations were chosen from every composition to construct the amorphous cell for subsequent MD

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simulation.

Once the amorphous cell was formed for each composition, it was subjected to 5 cycle thermal annealing from initial temperature of 300K to mid cycle temperature of 550K

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and then back to the initial temperature of 300K. Temperature and pressure were controlled by Andersen method with time step of 1 fs. After annealing, MD simulation was carried

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under isobaric condition using isothermal–isobaric ensemble (NPT) at 500K under the pressure of 1 bar for 5 ps with a time step of 1 fs. Thereafter, the system was cooled down to 80K in stepwise manner at the interval of 20K under same condition with a cooling rate of 4 K/ps. At each cooling step, temperature and pressure were controlled by Andersen and Berendsen methods respectively.

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2.2 Determination of parameters for blend miscibility: The Hildebrand solubility parameter (δ) is a prime factor indicating the attractive strength between the molecules to describe the blend miscibility. It was calculated from last

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few hundred picoseconds of the trajectory files and expressed as the square root of the cohesive energy density (CED).

δ = √CED

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(2)

CED represents the amount of energy required to separate the constituent atom or molecule to

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an infinite distance where its potential energy becomes zero and it includes electrostatic interactions, van der Waals interactions and hydrogen bond interactions [31]. Mathematically CED is defined by Eq. (3) [19,21],

CED =

V

m

 =

V 

m



(3)

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where ∆Ev=internal energy change of vaporization, ∆Hv=enthalpy of vaporization, Vm= molar volume of liquid at the temperature of vaporization, R= universal gas constant and T= absolute temperature. If (δA–δB)2 for polymers A and B is less than 4 J/cm3, the two polymers

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are expected to be miscible [32].

If the system is completely equilibrated, change in energy during mixing is expressed

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by Eq. (4),

coh

∆Emixing = ∅A 

A

coh

+ ∅B 

B

coh

−

mix

(4)

where ∆Emixing is the change in energy during mixing per unit volume, the terms in parenthesis represent the cohesive energy density of the pure polymers (A and B) and the blend (mix), and ∅A & ∅B represent the volume fractions of pure polymers in the blend. Finally, the Flory-Huggins interaction parameter can be evaluated by Eq. (5), 7|Page

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χ=

∆ mixing

Vmono



(5)

Eq. (5) gives both positive and negative value of χ. A positive χ does not always represent the immiscible blend. Besides it depends on the critical value of χ evaluated from Eq. (6), %

%



& √'(

+

&

%

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χ$ =

(6)

√')

where χ$ is the interaction parameter at critical point, nA and nB are the number of repeat units

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of polymer A and polymer B respectively. If χ ≤ χ$ , the blend is considered to be miscible. 2.3 Dissipative particle dynamics (DPD):

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In DPD method, a group of atoms or volume of fluid, which are represented by beads are larger than atomic level but smaller than macroscopic level. In this work the interacting beads follows the Newton’s equation of motion [33]. +,+.

= v0 ;

+2+.

= f0

(7)

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where ri and vi are the position and velocity of the ith bead respectively. fi represents the force when all the masses are normalized to 1. A polymer chain can be described by n454 , number of beads in DPD simulation.

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n454 =

67

68 98

=

'

98

(8)

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where MP represents the molar mass of the polymer, Mn represents the molar mass of the repeat unit, n is the total number of beads in a single polymer chain and Cn is the characteristic ratio of polymer which illustrates the number of repeat unit grouped together to form a bead.

The forces, fi, acting on the beads are governed by the three pair wise functions,

f0 = ∑=A0;F0=9 + F0=4 + F0= > + f0? + [email protected]

(9)

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where FijC is the conservative repulsive force which includes excluded volume effect, FijD is the dissipative force which includes the viscous drag between two moving beads and FijR is the random force which includes stochastic impulse. Other two terms indicate the bonded

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interactions where fiS represents bond stretching and fiA represents angle bending forces. Groot and Warren first introduced a good approximation for the pressure (p) in connection with number density or bead density (ρ) and maximum repulsion between the two interacting

p = ρk E T + αHρ&

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beads (a) [21].

(10)

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where co-efficient α = 0.101 . Based on the Eq. (10), dimensionless compressibility (k % ) could be expressed as.

k % = 1 + 2αHρ/k E T

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Introducing known compressibility of water, k % NO.P, = 16 in Eq. (11), repulsion (a) could be expressed as

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H = 75kE T/ρ

(12)

Any value can be chosen as number density in DPD simulation however larger value requires longer simulation time. As suggested by Groot and Warren [21], number density was taken as

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3 and hence H = 25k E T was reasonable parameter for liquids. The soft-sphere interaction in DPD is mapped on Flory-Huggins theory through

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interaction parameter. If the system has ith and jth bead interacting with each other where H00 = H== = 25k T T and (ρi + ρj) is approximately constant, the interaction parameter can be expressed as [21].

χ=

&U;V-W V-- >;X- YXW > Z) 

(13)

where (ρi+ρj) = ρ is the density of the system. The repulsion between the dissimilar beads could be given as [21],

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H[\ = H[[ + ∆H

(14)

where ∆H is excess repulsion and can be expressed as χN/∆H ∝ N , N is the length of the polymer chain.

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Assuming k E T = 1, the interaction between the similar types of beads was calculated as 25 i.e. aii = ajj = 25. If ∆H = 3.5χ `21a; Eq. (14) can be written as. H[\ = 25 + 3.5χ

(15)

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here interaction parameter (χ) was obtained from the atomistic simulation.

Determination of bead size and density: Mass of a bead could be expressed as Cb . [email protected] ,

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where Cb indicates characteristic ratio (number of repeat unit per bead) and [email protected] represents mass of the repeat unit. Here PA6 was taken as a reference and mass of a single bead was calculated to be 685 amu (6.06 ∗ 113.16 = 685). As bead mass was considered to be similar for both the polymers, so single bead represents 8.01 number of repeat units for FKM. (6.06 ∗ 113.16/85.5 = 8.01, where 85.5 amu is the repeat unit weight of FKM)

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Volume of one mole of bead could be given by Cb . [email protected] where [email protected] specifies molar volume of the repeat unit. In the present simulation, it was calculated to be 636.1 cc (6.06 ∗ 104.96 = 636.1) considering molar volume of PA6 is 104.96 cc at 298K; or volume of single bead was

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1056.1 Å3. As number density was taken as 3, the volume occupied by 3 beads was 3168.3

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Å3 (3 ∗ 1056.1 = 3168.3). Therefore, the length scale for reduced unit was calculated to be 14.69 Å.

The DPD simulation was performed for the 40/60 blend of PA6/FKM within the

cubic simulation box of length 500 Å with a bead mass of 685 amu and length scale of 14.7 Å in reduced unit. Ewald summation method was used for electrostatic interaction whereas bead based method was used for van der Waals interaction. The production run was 50000 steps with a time step of 1221.94 fs. Input parameter for DPD simulation is listed in Table 2.

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Table 2

Sample

Mp

Cn

ijkj

PA6

50000

6.06

73

FKM

100000

8.01

146

designation

3. RESULTS AND DISCUSSION:

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Input parameters of DPD simulation for 40/60 blend of PA6/FKM.

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Large number of repeat unit needs prolong simulation time and inaccurate result might come out due to calculation complexity, whereas short repeat unit might show end

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effects. Selection of total number of repeat units for atomistic simulation was based on solubility parameter [34]. Variation of solubility parameter with repeat unit for pristine

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polymers is plotted and shown below (Fig. 1).

Fig. 1.Variation of solubility parameter as a function of repeat unit for pristine PA6 and FKM. ( represents the solubility parameter of PA6 obtained for larger cell).

Fig. 1 shows that with the change in repeat unit, the solubility parameter does not

change significantly for the present systems. Even we utilized 6 chains of PA6 each of which contained 40 repeat units to construct the amorphous cell module and the solubility parameter shown by asterisk ( ) lies close to the other values. The density was estimated to be 11 | P a g e

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1.104 g/cc at 300K, same as the one determined for 5 chains in the cubic cell of PA6 40FKM 60. Thus, the cell size and the chain number of 5 were representative in the present investigation. As a consequence, repeats units per chain for the pristine polymers and number

amorphous cell models after the energy minimization.

(b)

(C)

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(C)

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(a)

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of chains were chosen according to the weight ratio of the blend. Fig. 2 represents the bulk

Fig. 2. Amorphous unit cell of (a) PA6, (b) FKM and (c) PA6 40FKM 60 at 300K, represented by element; carbon: grey, hydrogen: white, nitrogen: blue, oxygen: red and fluorine: sky.

In Figs. 2a and 2c, dotted lines represent the hydrogen bonds which are absent for

pristine FKM in Fig. 2b.The hydrogen bond is an attractive non bonded interaction between hydrogen atom of a molecule or a molecular fragments attached with more electronegative atom X (where X-H act as a donor) and an atom or an anion Y (act as an acceptor) in the same or different molecule [35]. A typical hydrogen bond may be depicted as X

H

Y.

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In addition to the intra and inter molecular hydrogen bonds between PA6 chains, some intermolecular hydrogen bonds are also formed between PA6 and FKM chains where N-H act as a donor and F atom act as an acceptor, as shown in Fig. 3. This may indicate some

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compatibility between the two polymers.

PA6

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H Bond

FKM

PA6

Fig. 3. Intermolecular Hydrogen bonds between PA6 and FKM chains in amorphous unit cell represented by element; carbon: grey, hydrogen: white, nitrogen: blue, oxygen: red and fluorine: sky.

3.1 Glass transition temperature:

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Although a distinct change in mechanical properties are observed through glass transition, the transition itself is not any kind of phase transition. Rather glass transition is a second order transition where segmental mobility of polymer chains starts upon heating,

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indicating the onset of rubbery behaviour. For polymer blends, single glass transition temperature (Tg) gives an indication of blend miscibility and can be determined according to

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the Fox equation [36,37].

%

l

=

m(

l(

+

m)

l)

(16)

where WA & WB are the weight fractions of polymer A and polymer B respectively and TgA & TgB are their respective Tgs in absolute scale. But the phenomenon is different for immiscible blends where two separate Tgs are observed corresponding to separate immiscible domains [38]. 13 | P a g e

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(b)

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(c)

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Fig. 4. Specific volume as a function of temperature for pure polymer and their blend. The Tgs were estimated at 336K and 250K for (a) pristine PA6 and (b) FKM respectively and two distinct Tgs were observed at 348K and 254K for (c) PA6 40FKM 60 corresponding to the Tg of PA6 and FKM respectively by MD simulation.

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Fig.4 represents the change in specific volume (reciprocal of density) with respect to temperature in absolute scale for pure polymers and their blend. Distinct inflection points

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were observed in each curve on cooling from higher temperature where the slope of the curve i.e. thermal expansion co-efficient altered, suggesting the occurrence of Tg. The Tgs estimated from the MD simulation were at 336K and 250K for pristine PA6 and FKM respectively as shown in Figs. 4a and 4b, whereas in Fig. 4c, two distinguishable inflection points were observed at 348K and 254K for the 40/60 blend of PA6/FKM, which reflected the intrinsic Tgs of PA6 and FKM respectively. The Tg for pristine polymers and their blend were consistent with the literature value [39]. These are depicted in Table 3. The simulation results also indicate immiscibility of the two polymers.

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Table 3 Glass transition temperatures of the pristine polymers and their blend measured by MD simulation from amorphous cell module and experimentally determined glass transition temperatures of the same (from DSC and DMA).

Tgrb ( MD simulation) (K) -

FKM

-

250

PA6 40FKM 60

348

254

Sample designation

glass transition temperature of plastic phase

b

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a

Tgpa Tgrb (experimental data) (experimental data) (K) (K) DSC DMA DSC DMA 337 320 269 248 259 315 323 242

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PA6

Tgpa ( MD simulation) (K) 336

glass transition temperature of rubber phase

3.2 Solubility parameter:

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Experimental data, taken from reference 39, were obtained from measurement in DSC (Differential scanning calorimetry) and DMA (Dynamic mechanical analyzer)

In the interest of determining the miscibility of PA6 and FKM, solubility parameter was measured for pristine polymers as well as their blend from the atomistic replica of the

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actual chains confined within the cubic simulation box using Forcite module. Simulation results are shown in Table 4 and the results are compared with those obtained by group contribution method, as given in van Krevelen’s book [40].

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Consistent results were obtained from the MD simulation for the prediction of solubility parameter when compared with the group contribution theory for the same.

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Deviation between group contribution theory and MD simulation was more for PA6. This can be attributed to the occurrence of hydrogen bonding in PA6 which cannot be adequately described in group contribution method. Similar results were also found by Gupta et al. for the pharmaceutical compounds [32]. It was also evident from Table 4 that the blends of PA6 and FKM were likely to be immiscible, as ∆δMDSimulation was greater than 2 (J/cm3)0.5.

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Table 4 Solubility parameter of pristine PA6 and FKM determined by group contribution method (proposed by D.W. van Krevelen) and by MD simulation.

δvanKrevelen (J/cm3)0.5

δMD Simulation (J/cm3)0.5

PA6

25.1

21.8 ± 0.297

FKM

13.8

14.2 ± 0.273

∆δMDSimulation (J/cm3)0.5

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Sample designation

7.6

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Alternatively from Eq. (5), interaction parameter of the blends was calculated considering the realistic mixing and demixing system. The results are represented in Table 5.

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Table 5 Interaction parameter of 40/60 blend of PA6 and FKM.

Sample designation PA6 FKM

% Weight in the blend 40 60

Volume fraction (φ)

∆Emix (J/m3)

χ

χexperimental

0.53 0.47

0.0929* 108

0.25

0.23

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Interaction parameter as manifested in Table 5 was higher than the critical value of same (no = 0.0243) calculated according to Eq. (6). This result again gave a clear indication of immiscibility of the blend and as a consequence of this, two distinct inflection points were

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observed in specific volume vs temperature plot in Fig. 4c. Interaction parameter measured from the atomistic simulation was consistent with the experimentally calculated value of the

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same obtained from interfacial tension between the rubber and the thermoplastic phase [13]. We have also looked into the contribution of van der Waals forces and electrostatic

forces to the net solubility parameter. The results are highlighted in Table 6. Comparison of the magnitude of different forces revealed that the van der Waals forces contributed more to the total solubility parameter for both the pristine polymer and their blend. However the van der Waals dispersive force was higher for PA6 owing to more linear chains [41]. In contrast,

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FKM preferred to form coiled structure with smaller surface area as compared to PA6 (Figs. 2b and 2c). Table 6

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Contribution of van der Waals and electrostatic forces to solubility parameter in MD simulation.

δvan der Waals (J/m3)0.5

δElectrostatic (J/m3)0.5

PA6 FKM PA6 40FKM 60

18.092 11.788 12.523

11.385 7.309 6.597

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Sample designation

3.3 Role of energy component in the transition of glassy to rubbery state:

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In order to assess the effect of different interacting components on glass transition, various energy components were plotted against temperature. The representative results are depicted in Figs.5 and 6. (a)

(c)

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(b)

Fig. 5. Plot of van der Waals (non-bonded) energy vs temperature in absolute scale. (a) PA6, (b) FKM and (c) PA6 40FKM 60. 17 | P a g e

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(b)

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(c)

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Fig.6. Plot of torsion energy vs temperature in absolute scale. (a) PA6, (b) FKM and (c) PA6 40FKM 60.

In the simulation results, inflection points were found in the case of van der Waals energy and torsion energy while plotted against temperature for pure polymers near the

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glassy to rubbery transition, whereas above and below the glass transition, these two energy components increased linearly with temperature. However, for the 40/60 blend of PA6/FKM,

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two inflection points were observed for the van der Waals energy and torsion energy components as shown in Figs. 5 and 6 respectively. These results reflected that the van der Waals energy and dihedral torsion energy are the major contributors to the glass transition. The occurrence of the inflection points are the results of freezing of polymer chains below glass transition. Stretching energy and bending energies have no effect at the glass transition, as these appeared to be linear with temperature without giving any inflection point. Yang et

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al. also found similar results in the case of poly(3-hydroxybutyrate) and poly(ethylene oxide) by MD simulation [42].

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3.4 Polymer chain dynamics: In order to look into the dynamics of PA6 and FKM chains in this system, mean-

polymers as well as their blend. MSD = 〈|rttv − rt0v|& 〉= 6Dt

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square displacements (MSD) were estimated from the MD simulation at 300K for pristine

(15)

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where rttv and rt0v are the position of the centre of mass of the chains at time t and 0 respectively and the slope of the curve D represents diffusion co-efficient. Fig. 7 illustrates the MSD of PA6 and FKM chains in pure form and in the blend. In contrast to the pristine polymers, mobility of PA6 chains was higher than FKM in blend system as observed from

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the slope of the MSD curve. These results indicated the faster relaxation of PA6 chains in the presence of FKM which suggest the increase in crystallization rate of PA6 as FKM chain can act as a nucleating agent. Abreu et al. also mentioned similar observation for polypropylene/styrene-butadiene-styrene

and

polypropylene/styrene-ethylene/1-butene-

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styrene blends [43]. On the other hand, mobility of FKM chains decreased due to presence of

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crystalline PA6.

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Fig. 7. Mean-square displacements of PA6 and FKM chain for pristine polymers and their 40/60 PA6/FKM blend at 300K

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3.5 Morphology:

From atomistic simulation, Flory-Huggins interaction parameter χ for 40/60 blend of PA6/FKM was found to be 0.25 at 300K which was higher than that of its critical value. We have also found two distinct inflection points in specific volume vs temperature plot. Both of

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these results gave an indication of immiscible morphology of the 40/60 blend of PA6/FKM. Morphology developed by DPD simulation (Fig. 8a) also illustrated the existence of PA6 matrix and FKM rich domains which clearly indicated the immiscibility of the blend. On

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close observation, it was found that FKM domains represented by black were dispersed in the PA6 depicted by white. The simulated morphology was in line with FESEM image (Fig. 8b)

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and AFM image (Fig. 8c) of the 40/60 blend of PA6/FKM previously discussed by our research group [33]. Mean diameter of the rubber phase from DPD simulation (Fig. 8a) showed close proximity with the FESEM and AFM analysis (Figs. 8b and 8c respectively) as listed in Table 7. The slightly lower value in the simulation results may arise due to lower molecular weight of pristine polymers taken.

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Fig.8. Morphology of 40/60 blend of PA6/FKM, (a) FKM density profile after 50000 steps DPD simulation; PA6: white, FKM: black, (b) FESEM analysis; PA6: dark colour, FKM: white and (c) AFM analysis; PA6: dark brown, FKM: light yellow.

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Table 7 Mean diameter of disperse rubber phase from DPD simulation, FESEM and AFM images.

Mean diameter (Simulation) nm

Mean diameter (FESEM) nm

Mean diameter (AFM) nm

PA6 40FKM 60

32 ±11

72 ±25

53 ±17

4. CONCLUSIONS:

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In this paper, full atomistic simulation was adopted in order to predict the miscibility

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of PA6 and FKM along with the mesoscale modelling of 40/60 blend of PA6/FKM to examine the morphology. From the temperature dependence of specific volume plot, single

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glass transition temperature was found for pristine polymer, whereas 40/60 blend of PA6/FKM exhibited two glass transition temperatures indicating the immiscibility of the blend. Glass transition temperatures obtained from the MD simulation were found to be consistent with the experimental results. Again Flory-Huggins interaction parameter χ also

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supported phase separation owing to the positive deviation of χ from its critical value at 300K. Dihedral torsion and van der Waals energy exhibited similar behaviour and played a major role in the glass transition temperature. The dynamics of polymer chains indicated an

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increase in mobility of PA6 in presence of FKM resulting in faster crystallization rate of PA6. Morphology predicted by the DPD simulation method also demonstrated the immiscibility of

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the rubber and the plastic in the blend and the results were comparable with FESEM and AFM analysis. The simulation & experimental results can be summarized in Fig. 9 along with the deviation plot of Tg.

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Tg.

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Fig. 9. Comparison between computer simulation and experimental results along with deviation plot

ACKNOWLEDGMENTS

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We are thankful to IIT Kharagpur (affiliated institute) for giving the facilities. We are also

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grateful to Dr. Shib Shankar Banerjee for providing the FESEM and AFM images.

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The key points of the present work are emphasized below: Molecular dynamic simulation was applied for the first time to thermoplastic elastomers from rubber –plastic blend.



Spatial disposition of polymer chains in a cubic simulation box was highlighted.



The glass transition temperature from specific volume vs temperature plots for both pristine polymers and their blends was predicted. The results were in line with those obtained from different experimental techniques.



Solubility parameter of polymers was estimated , which was further used to evaluate interaction parameter in the blend system. The result was compared with the experimental values.



Morphology of the blend generated by Dissipative Particle Dynamics (DPD) simulation was in accord with the AFM and FESEM observations.

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