Phenomenological study of the isotope effect on the equilibrium melting point of polymer crystal

Accepted Manuscript Phenomenological Study of the Isotope Effect on the Equilibrium Melting Point of Polymer Crystal Sreenivas Kummara, Kohji Tashiro PII:

S0032-3861(15)30337-2

DOI:

10.1016/j.polymer.2015.10.051

Reference:

JPOL 18218

To appear in:

Polymer

Received Date: 11 July 2015 Revised Date:

21 October 2015

Accepted Date: 23 October 2015

Please cite this article as: Kummara S, Tashiro K, Phenomenological Study of the Isotope Effect on the Equilibrium Melting Point of Polymer Crystal, Polymer (2015), doi: 10.1016/j.polymer.2015.10.051. 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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Graphical Abstract

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Phenomenological Study of the Isotope Effect on the Equilibrium Melting Point of Polymer Crystal

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Sreenivas Kummara and Kohji Tashiro*

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Hm

Dn

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(Revised)

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Phenomenological Study of the Isotope Effect on the Equilibrium Melting Point of Polymer Crystal

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Sreenivas Kummara and Kohji Tashiro*；

Department of Future Industry-Oriented Basic Science and Materials, Toyota Technological Institute, Tempaku 468-8511, Japan

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Abstract

The equilibrium melting point (Tom) or the ultimate melting point of a polymer

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crystal is different between the hydrogeneous (H) and dueterated (D) species, as exemplified for the various cases of polyethylene, isotactic polypropylene,

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polyoxymethylene and so on.

The present study has focused on the specific case of

the blend samples of hydrogeneous and deuterated polyoxymethylenes (POM-H [-(CH2O)n-] and POM-D [-(CD2O)n-]) and the random copolymers between the CH2O and CD2O monomeric units.

As the POM-H samples, the homopolymers composed of

H-trioxane monomeric units and the copolymer containing a small amount of ethylene

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oxide (EO-POM copolymer) were used since these two samples were different in the The Tom of the blend samples was found to change continuously

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melting point.

depending on the D/H content, although the content dependence was different between the blend samples of POM-D with POM-H homopolymer and those of POM-D with

Such an isotopic effect on Tom has been interpreted reasonably on the

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also remarkably.

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EO-POM copolymer. The Tom of the D/H random copolymers was found to change

basis of the thermodynamic equations derived with the statistical probabilities of the D and H component distributions taken into account.

The agreement between the

experimentally-evaluated values and the theoretically-estimated values is good for the

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Tom in both the cases of D/H blends and D/H random copolymers.

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Keywords

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Polyoxymethylene, equilibrium melting point, isotope effect

Introduction

Polymer isotopes are sometimes utilized in the study of crystallization, phase

separation etc [1].

For example, a small amount of deuterated atactic polystyrene

[D-PS, -(CD2CD(C6D6))n-] was mixed with the hydrogeneous polystyrene [H-PS,

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-(CH2CH(C6H6))n-] or vice verse [2-3]. The thus-prepared D/H PS blend samples were

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quite useful for the evaluation of the spatial dimension of a single chain in the amorphous phase by the measurement of small-angle neutron scattering (SANS), since

the high contrast is obtained between the D and H chains due to their remarkably As for the crystalline polymers,

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different neutron scattering cross sections [4].

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similarly, the SANS experiment was performed in the crystallization process from the melt to reveal the dimensional change from the random coil in the melt to the folded chain form in the crystalline lamella [1].

Typical case was reported for the blend

samples of deuterated high-density polyethylene [DHDPE -(CD2CD2)n-] and However, the

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hydrogenous high-density polyethylene [HDPE -(CH2CH2)n-] [3, 5-7].

blend between DHDPE and HDPE was not necessarily suitable for this purpose since

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the mixture of the D and H species shows a partial phase separation when slowly cooled from the melt [3, 5-7].

In other words, the perfect cocrystallization cannot be attained

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for this pair, making the discussion ambiguous more or less.

Almost perfect

cocrystallization was found for a pair of DHDPE and linear-low-density polyethylene (LLDPE) with small amount of short branches (for example, 17 ethyl branches per 1000 skeletal carbon atoms) even when cooled slowly from the melt [8-14].

In fact, using a

series of the various blend samples of DHDPE and LLDPE, the experimental data of

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infrared spectra and SANS revealed successfully the spatial distribution of chains in the The molecular chain does not change the

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crystallization process from the melt [14].

dimension very much during the crystallization, and the D-PE and H-PE stems are

randomly arrayed in the lamella, so the molecular chain is folded randomly on the

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lamellar surface, supporting the concept of random reentry mechanism of chains.

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Another point to be noticed is the difference in the melting point and melt-crystallization rate between the D and H species.

In the case of above-mentioned

DHDPD/LLDPE blends, the melting point was detected as a single peak and the peak position shifted continuously depending on the D/H content.

The similar phenomenon The

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was observed for isotactic polypropylene [it-PP, -(CH2CH(CH3))n-] [15-17].

melting point between the D and H species is different: 153°C for D-species and 156°C The crystallization rate was also found different remarkably between

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for H-species.

these two species.

The D- and H-species of it-PP were found to cocrystallize when

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cooled slowly from the melt.

The infrared spectra of the D/H blend samples were

utilized to clarify the intermolecular interactions and the packing mode of the polymer chain stems [14-18].

In this way, the isotopically-different polymer species is quite useful for the structural study from the various points of view.

It is important to notice that the

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melting point is remarkably different between the D and H polymer species by a For example, the melting point of DHDPE is 127°C and that of

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detectable amount.

HDPE is 136°C [5-7]: the difference of melting point (mp) between the D and H species (mp((H) – mp(D)) is about 9oC.

These large isotopic effects of melting point of polymer is

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already mentioned above.

In the case of it-PP, the mp difference is about 3oC, as

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highly contrast to the case of small molecules such as benzene, which shows very small difference in melting point between the D and H species (~1 oC) [19].

The

covalently-bonded array of D monomeric units along the polymer chain is considered to cause the cooperative effect or the so-called polymer effect on the melting point by

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accumulating the small difference of chemical potential between the D and H monomeric units several thousand times.

The evaluation of an ultimate melting point

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or the equilibrium melting point (Tom) is needed for understanding the remarkable isotope effect on the thermodynamic property of the polymer [20].

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In the present paper we focus on polyoxymethylene (POM).

The remarkable

difference in the melting point was found between the D and H species: 165°C for POM-H [-(CH2O)n-] and 178.5°C for POM-D [-(CD2O)n-] [21, 22].

In our previous

paper [22], a phenomenological treatment was performed to interpret such an isotope effect on Tom with the probability of spatial arrangement between the D and H stems in

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the common lattice taken into account.

Quite recently, we have succeeded to

D/H contents.

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synthesize the random copolymers between D-trioxane and H-trioxane with the various The thus-polymerized samples are not the random copolymers between

D- and H-trioxanes but the random copolymers between CH2O and CD2O units.

The

It may be a good chance to investigate the isotope effect on the

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the D/H content.

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melting point and the crystallization rate were found to sensitively change depending on

melting point in more detail since both the D/H blend samples and the D/H random copolymers have been obtained for POM.

In the present study, the isotope effect on Tom of POM is interpreted

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phenomenologically for a series of POM-D and POM-H blend samples as well as the D/H random copolymers.

The detailed study of the thermodynamic property of

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isotopically different POMs is needed as a basic information in the research of the chain aggregation in the melt and the spatial array of individual chains in the crystalline

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lamella by performing the SANS and FTIR spectral measurements.

The utilization of

D and H blend samples of POM might be useful for the confirmation of our previous studies which reported the generation of taut tie chains passing through the neighboring lamellae [23-25], that is to say, we might expect that the D-tie chains might be distinguished from the matrix of H-chains.

The isotopic effect on the crystallization

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rate of POM will be reported in a separate paper.

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Before the description of the experimental data and their theoretical interpretation, it is needed to point out that the commercially-available POM-H samples must be

distinguished strictly between the homopolymer (Delrin, for example) and the

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copolymer including some amount of comonomer (Duracon, for example).

In our

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previous paper the POM-H with ethylene oxide (EO) 2.2 mol% was utilized in the study of isotropic effect on the melting point of POM-D and POM-H samples. However, the D/H random copolymers to be treated here do not contain any such third comonomer component as EO in the samples.

The melting point between the homopolymer and Therefore, in the present paper,

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EO-copolymer is about 5oC different from each other.

we have to investigate the isotopic effects on the melting behaviors for the following 3

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sets of the POM samples:

(i) a series of D/H copolymers without any EO comonomer units,

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(ii) a series of blend samples between POM-D and POM-H (Delrin-type homopolymer) and

(iii) a series of blend samples between POM-D and POM-H with small amount of EO comonomer units (EO-POM-copolymer).

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Experimental Section The samples utilized in the present paper are listed in Table 1.

The

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Samples

POM-H samples were Delrin 100 and 500, both of which were homopolymers of trioxane, and Duracon (M90), a copolymer containing EO unit of 2.2 mol%.

The

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POM-H homopolymer sample (H100), which was synthesized by ourselves using the

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similar technique to that of D/H random copolymers described below, was also included in this table. The D/H random cppolymers (and the POM-H sample) were synthesized in the present study.

The D/H molar ratios were 100/0, 69/31, 48/52, 29/71 and 0/100.

The details of the synthesis were described in a separate paper [26].

Briefly speaking

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about the process, the copolymers were synthesized by the cationic polymerization reaction for a mixture of H-trioxane and D-trioxane in the dried cyclohexane solution,

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where small amounts of boron trifluoride butyl ether and butyl ether were added as a catalyst [26].

The end OH units were capped by acetic acid to stabilize the sample

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from the thermal degradation in the molten process.

The randomness of CH2O and

CD2O units in the chain was confirmed on the basis of high-resolution

13

(nuclear

deuterated

magnetic

resonance)

hexafluoroisopropanol solutions. D/H copolymers.

spectral

data

measured

for

the

C NMR

The 13C NMR spectra were measured for a series of

As shown in Figure 1, the peaks of 13CD2 unit split into 5 peaks due

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to the spin-spin couplings between

13

C and D magnetic spins.

That is to say, the positions of the

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were noticed to consist of fine peaks individually.

Besides, the 5 peaks

original 5 peaks were shifted toward the lower magnetic field side corresponding to the

various sequences (triad) of CD2O-CD2O-CD2O (DDD), CD2O-CD2O-CH2O (DDH) The integrated

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and CH2O-CD2O-CH2O (HDH), as illustrated in Figure 1 (b).

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intensities of these finely-split peak components gave the fractions of diad (DD, DH and HH) and triad sequential probabilities of CD2O and CH2O units.

From these

values, the so-called run number R was calculated, which is defined as the number of boundary between the H and D monomer sequences included in the chain of 100 For example, R = 3% in the sequence of D35-H30-D15-H20, and R

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monomer units [27].

= 10% for the sequence D10-H3-D10-H20-D5-H3-D10-H20-D4-H5-D10. The Rs of the D/H These R values

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copolymers were calculated from the diad values as listed in Table 1.

were compared with those predicted for the various such models as random copolymer

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of CD2O and CH2O units, block copolymer -(CD2O)n-(CH2O)m- and alternating

copolymer of CD2OCH2O sequence.

As seen in Table 1, the R values of the POM

copolymers are in good agreement with those predicted for the copolymer consisting of random sequence of CD2O and CH2O units.

That is to say, the copolymers used here

are not the random copolymers between the D- and H-trioxane monomeric units

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[(CH2O)3 and (CD2O)3] but they are the random copolymers of the CH2O and CD2O The blend samples between POM-D and POM-H chains were prepared for the

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units.

pairs of POM-D and H100 as well as those of POM-D with Duracon. The blending molar ratios of D and H monomers were 100/0, 69/31, 48/52, 29/71 and 0/100.

The

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blend samples were prepared by casting from the hexafluoro-isopropanol (HFIP)

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solutions.

The molecular weights of all these samples were measured using a SEC method with HFIP as a solvent, where the Toso HLC-8229GPA with two Super HM-M columns was used for the measurement and the molecular weights (Mn and Mw) were estimated

Evaluation of Tom

The results are shown in Table 1.

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in terms of poly(methyl methacrylate)s.

The samples were isothermally crystallized from the melt at the

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various constant temperatures to get the unoriented samples having the different lamellar sizes.

The lamellar thickness L was estimated using small-angle X-ray

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scattering (SAXS) data, in which the correlation function of the stacked lamellae was calculated and the averaged lamellar thickness was estimated [28].

A Rigaku

Nanoviewer X-ray diffractometer was used for the SAXS measurement using a Cu-Kα

beam line.

The melting points Tm of these bulk samples were measured with a TA

Q1000 differential scanning calorimeter at the heating rate of 5oC/min. The plot of Tm

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against 1/L gave the Tom on the basis of Gibbs-Thomson equation [20].

where K is a constant.

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Tm = Tom - K/L In the usage of this equation, we assumed that the lamellar

thickness (L) was not changed in the heating process up to the melting point.

Some

The homopolymer, i.e., Delrin 100, Delrin 500 and H100 gave the

same Tom of about 190oC.

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samples were used.

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examples of Gibbs-Thomson plot are shown in Figure 2, where a series of POM-H

The difference in molecular weight does not influence the

Tom value, since it is a melting point of infinitely thick lamella.

The Tom of Duracon,

about 184oC, is a little lower than them because of the existence of EO units in the

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lattice.

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Results and Discussion

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D/H Content Dependence of Tom (i) D/H random copolymers Figure 3 shows the Tom evaluated experimentally for a series of D/H random

copolymers.

Here the data measured for POM-H homopolymer and POM-D samples

were also included at the points of D = 0 and 100 mol%, respectively.

In the case of

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POM-H homopolymers, as shown in Figure 2, the Tom was essentially the same among

molecular weight (Table 1).

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the different species (Delrin 100, Delrin 500 and H100) in spite of the difference in The similar situation may be said also for the D/H

copolymers and POM-D samples, although the molecular weights of these samples

In other words, we can say that the

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were more or less different as seen in Table 1.

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comparison of Tom can be made reasonably by focusing only the isotope effect between the D and H species as long as the molecular weight range is not very wide (Mn = 20000 ~ 70000).

The Tom is the highest for the POM-D sample and decreases almost linearly

with a decrement of the D content, and changes to plateau near the POM-H content.

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(ii) Blend samples between POM-D and POM-H Homopolymers

Figure 4 shows the D/H blend ratio dependence of Tom measured for a series of The Tom decreases

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blend samples between POM-D and POM-H homopolymer (H100). with a small curvature, different from the case of the D/H copolymers.

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(iii) Blend samples between POM-D and EO-POM copolymer Figure 5 shows the D/H blend ratio dependence of Tom of a series of blend

samples between POM-D and EO-POM copolymer with a small amount of EO monomeric units (Duracon). previous paper [22].

This data is essentially the same as that reported in the

The Tom decreases with a small upward curvature as the POM-D

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content decreases.

The Duracon has a melting point 5oC lower than the homopolymer As a

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because of the inclusion of EO units in the crystallites (compare with Figure 4).

result, the Tom is also lower even at the ultimate state of infinitely large crystallite size.

This is different from the above-mentioned case of homopolymer samples with the

As already pointed out in Figure 3, all the samples of pure

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different molecular weight.

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POM-H with different molecular weight approach the same Tom at the infinitely large crystallite since the packing state of chains is not disordered, different from the cases of EO-POM copolymers.



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It must be noticed here that the melting peak detected in the DSC measurement of the blend samples was always a single peak, the position of which shifted

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continuously with the D content, indicating the D and H chains cocrystallize together in the common lattice although the D content dependence is different more or less

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depending on the type of POM-H sample component. The Tom is thermodynamically expressed by using the change in enthalpy (∆Hm)

and entropy (∆Sm) as below. Tom = ∆Hm/∆Sm = (Hm - Hc)/(Sm - Sc)

(1)

where Hm and Hc are the enthalpy of the melt and crystal, respectively, and Sm and Sc are

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the corresponding entropies.

Therefore the difference in Tom among the various D/H The ∆Hm

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samples originates from the D-content dependence of ∆Hm and ∆Sm in eq 1.

may be assumed almost equal irrespective of the D/H content, since the intermolecular interactions are essentially the same between the H and D species in the first On the other hand, the ∆Sm may be varied sensitively depending on

the D content.

In general, the ∆Sm is contributed by many factors including the

conformational

entropy

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approximation.

(∆Sconf),

the

vibrational

entropy

(∆Svib)

and

the

statistically-irregular arrangement of the D and H monomeric units or D and H chain stems in the crystalline lamellae (∆Sarray).

Among them, ∆Sconf is mainly governed by

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the conformational distribution in the melt but it is not very much affected by the small mass difference between CD2O and CH2O units.

Rather, such mass difference may

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give the difference in the vibrational entropy Svib of the crystal phase. estimation of Svib was limited in the literature.

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reported for hydrogeneous polyethylene [29, 30].

The theoretical

For example, the Svib calculation was The inelastic neutron scattering was

measured for POM-D sample to get the density of vibrational state [31].

The

vibrational frequency-phase angle dispersion curves and the density of state were calculated using a POM single chain for comparison with the data observed by neutron scattering, but Svib was not estimated yet [32]. The random arrangement of the D and

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H species in the crystal lattice affects the ∆Sarray.

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The discussion made here can be applied also to the blend samples between POM-D and EO-POM copolymer.

The EO comonomeric units are considered to

coexist in the crystalline region of POM segments, but the interaction terms or the Hc

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and ∆Hm may be almost the same as those of homo-POM sample judging from the

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X-ray diffraction data which shows the crystalline peaks at almost the same positions between these two types of POM-H samples.

The phenomenological treatment of eq 1 is now described in the following sections

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by taking these matters into account.

Phenomenological Interpretation of D/H Content Dependence of Tom

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(1) D/H Blend Samples

The equation of Tom was already derived in the previous paper for a series of D/H

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blend samples [22].

The brief description is made here, which is helpful for

understanding the essential feature of our theoretical treatment.

The molar content of

POM-D chains is X. As illustrated in Figure 6 (a), the probability for the D chain

stems to be positioned side by side in the crystal lattice (D…D) is given as X2. Similarly, the probabilities of the side-by-side arrays of H…H stems and H…D stems

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are given, respectively, as (1-X)2 and 2X(1-X).

Therefore, the averaged enthalpy

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change ∆Hm at Tom is expressed as ∆Hm = X2∆Hm(DD) + (1-X)2∆Hm(HH) + 2X(1-X)∆Hm(HD)

(2)

where ∆Hm(DD), ∆Hm(HH) and ∆Hm(HD) are the enthalpy changes of the D…D, H…H Similarly, the melting entropy ∆Sm at Tom is given as

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and H…D pairs, respectively.

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∆Sm = X2∆Sm(DD) + (1-X)2∆Sm(HH) + 2X(1-X)∆Sm(HD)

(3)

Using eqs 2 and 3, the melting point Tom is expressed as

X2∆Hm(DD) + (1-X)2 ∆Hm(HH) + 2X(1-X)∆Hm(HD) Tom = ∆Hm/∆Sm =

(4)

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X2∆Sm(DD) + (1-X)2 ∆Sm(HH) + 2X(1-X)∆Sm(HD)

As already mentioned, the enthalpy changes ∆Hm(DD), ∆Hm(HH) and ∆Hm(HD) may be The melting points of the hypothetical groups

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assumed almost the same to each other.

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of D…D, H…H and H…D chain stems are defined, respectively, as Tom(DD) ≡ ∆Hm(DD)/∆Sm(DD)

Tom(HH) ≡ ∆Hm(HH)/∆Sm(HH)

and

Tom(HD) ≡ ∆Hm(HD)/∆Sm(HD).

As a result, the Tom is finally given by 1/Tom = X2/Tom(DD) + (1-X)2/Tom(HH) + 2X(1-X)/Tom(HD)

(5)

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(iii) The case of blend samples between POM-D and EO-POM copolymer The experimentally-evaluated Tom(DD) (= 481.7 K for POM-D) and Tom(HH) (= 457.3 K for EO-POM) were substituted in eq 5.

The solid curve shown in Figure 5 is the calculated one, which fits well to

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477.0 K.

The parameter Tom(HD) was assumed as

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the observed data.

(ii) The case of blend samples between POM-D and POM-H homopolymer The Tom(DD) is 481.7 K for POM-D as already mentioned.

These values were substituted into eq 5.

As shown

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homopolymer (H100) is 462.7 K.

The Tom(HH) for

in Figure 4, the experimentally-evaluated Tom were fitted well by choosing the

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parameter Tom(HD) as 482.0 K.

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(i) D/H Random Copolymers

In the case of D/H random copolymers, the probability Pn to create a sequence

-(D)n- in the copolymer is given as Pn = Xn where X is the D molar content (refer to the following picture).

(6-1)

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…… - H - H - D - D -….- D - D - H - H -…- H - H - D -…..

X(1-X)

Xn

X(1-X) (1-X)m

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… 1-X 1-X X X … X X 1-X 1-X … 1-X 1-X X …

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Similarly, the probabilities for -(H)m- (Pm) and HD (DH) segments (PHD) are expressed,

Pm = (1-X)m

(6-2)

PHD = 2X(1-X)

(6-3)

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Therefore, the ∆Hm is expressed as

∞

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respectively, as

∞

∆Hm = (ΣX )∆Hm(DD) + (Σ(1-X)m)∆Hm(HH) + 2X(1-X)∆Hm(HD) n

n=0

m=0

+ ∆Hm(HH)/X + 2X(1-X)∆Hm(HD)

(7)

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= ∆Hm(DD)/(1-X)

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Here, the ∆Hm(DD) is assumed to be the same as that used for the aggregation of D…D chains in the blend.

Such a common usage of the enthalpy changes is based on the

assumption that the finite sequences -(D)n- in the D/H copolymer chains are arrayed

side by side to form the regularly packed D unit regions, as illustrated in Figure 6 (b). This model is called here the model 1. change.

The similar expression is given for the entropy

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∞

∞

∆Sm = (ΣX )∆Sm(DD) + (Σ(1-X)m)∆Sm(HH) + 2X(1-X)∆Sm(HD) n

m=0

= ∆Sm(DD)/(1-X)

+ ∆Sm(HH)/X + 2X(1-X)∆Sm(HD)

(8)

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n=0

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Then the melting point is given by

∆Hm(DD)/(1-X) + ∆Hm(HH)/X + 2X(1-X)∆Hm(HD) Tom

= ∆Hm/∆Sm =

(9)

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∆Sm(DD)/(1-X) + ∆Sm(HH)/X + 2X(1-X)∆Sm(HD)

For the enthalpy change, we assumed that ∆Hm(DD) = ∆Hm(HH) = ∆Hm(HD), and

∆Hm(HD)/∆Sm(HD).

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Tom(DD) ≡ ∆Hm(DD)/∆Sm(DD), Tom(HH) ≡ ∆Hm(HH)/∆Sm(HH) and Tom(HD) ≡ Then, we obtain the following equation finally.

1/Tom = [X/Tom(DD)+(1-X)/Tom(HH)+2X2(1-X)2/Tom(HD)]/[1+2X2(1-X)2]

(10)

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The X dependence of Tom of the D/H random copolymer was calculated by setting the

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following values for Tom(ij) where i and j = D or H. Tom(DD) = 481.7 K, Tom(HH) = 462.7 K, and Tom(HD) = 465.0 K

The result obtained for the model 1 is shown with a broken line in Figure 3. The above-mentioned assumption that the particular sequences like -(D)n- are

arrayed side by side, as illustrated in Figure 6 (b), might be difficult to realize in an actual crystal of the copolymer.

It might be needed to introduce the probability Pnn’ for

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the side-by-side array of -(D)n- and -(D)n’- sequences (see Figure 6 (c), model 2), which

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may be given as Pnn’(DD) = XnXn’

(11-1)

The similar expression is obtained also for Hm…Hm’ groups arrayed side-by-side.

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Pmm’(HH) = (1-X)m(1-X)m’

(11-2)

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The probability of side-by-side arrangement of Dn…Hm is Pnm(DH) = 2*(X)n(1-X)m’ As a result, the ∆Hm is given by

∞∞

(11-3)

∞∞

∆Hm = (ΣΣX X )∆Hm(DD) + (ΣΣ(1-X)m(1-X)m’)∆Hm(HH) n, n’=0

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n n’

m, m’=0

=∆Hm(DD)/(1-X)

+ [2ΣΣ(X)n(1-X)m’+2X2(1-X)2]∆Hm(HD) n=0 m=0

+ ∆Hm(HH)/X2 + [2/(X(1-X))+2X2(1-X)2]∆Hm(HD)

(12)

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2

∞∞

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where the forth term is needed to express the CH2O-CD2O boundary along the chain.

Similarly,

∞∞

∞∞

∆Sm = (ΣΣXnXn’)∆Sm(DD) + (ΣΣ(1-X)m(1-X)m’)∆Sm(HH) n, n’=0

m, m’=0

∞∞

+ [2ΣΣ(X)n(1-X)m’+2X2(1-X)2]∆Sm(HD) n=0 m=0

ACCEPTED MANUSCRIPT 21

2

+ ∆Sm(HH)/X2 +[2/(X(1-X))+2X2(1-X)2]∆Sm(HD)

(13)

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=∆Sm(DD)/(1-X)

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Then, the melting point is given as

TE D

which is rewritten as below.

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∆Hm(DD)/(1-X)2+∆Hm(HH)/X2+[2/(X(1-X))+2X2(1-X)2]∆Hm(HD) Tom = ∆Hm/∆Sm = (14) 2 2 2 2 ∆Sm(DD)/(1-X) +∆Sm(HH)/X +[2/(X(1-X))+2X (1-X) ]∆Sm(HD)

1/Tom=[X2/Tom(DD)+(1-X)2/Tom(HH)

(15)

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+2(X(1-X)+X4(1-X)4)/Tom(HD)]/[X2+(1-X)2+2(X(1-X)+X4(1-X)4)]

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The curve calculated for this model 2 is given by a solid line in Figure 3, where the same Tom(HD) value was used, 465.0 K, as that used in the calculation of model 1. The agreement of the calculated curve with the experimentally-evaluated Tom

values is better for the model 2, although the difference is not very large compared with model 1.

As shown in Figure 6 (c), the random arrays of the D and H segments of the

copolymer chains in the crystal lattice or the model 2 is more natural than the model 1.

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The hypothetical Tom of the D…H pairs is different between (i) D/H random copolymers (model 2), (ii) D/H(homopolymer) blends, and (iii) D/H(EO-copolymer) blends: Tom = 465.0 K, 482.0 K and 477.0 K, respectively.

As already pointed out, the Tom itself

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H…D pairs are between the neighboring chains.

In the cases of blends, the

(Duracon). blends.

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is different by 5oC between homopolymer (Delrins and H100) and EO-POM copolymer The Tom(HD) has also the same tendency between these two types of In the case of D/H copolymers, the H…D pairs must be considered for both

of intramolecular and intermolecular units.

If the ∆Hm is common to both the D and H

TE D

units as assumed above, the difference in Tom(DH) might come from the difference of ∆Sm(HD) between the blend and copolymer cases.

As discussed above, the entropy It is now difficult to

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term is governed by the many factors (∆Sconf, ∆Svib, ∆Sarray, …).

extract the most significant term for the interpretation of Tom(DH) of the copolymer.

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(3) Contribution of Entropy Terms In Figures 3 - 5, we notice that the plot of Tom vs X is curved in the upward

direction for the cases of D/H blends, while the plot is curved downward in the copolymer case.

These differences come from the difference in the contribution of the

third term in eqs 5, 10 and15, in other words, the contribution of the entropy term

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related to the probability of the side-by-side array of the same or different kinds of

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isotope species as understood from eqs 3, 8 and 13. The contribution of each entropy term (∆Sm(DD), ∆Sm(HH) and ∆Sm(DH)) is derived for the two types of blend samples and the copolymer models 1 and 2.

Since

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the enthalpy change ∆Hm was assumed to be the same for all the D/H blends and Therefore, the contributions

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copolymers, the entropy change is proportional to 1/Tom.

of entropy terms can be calculated using eqs 5, 10 and 15 for the blend samples and copolymer models 1 and 2, respectively.

The results are shown in Figure 7 (a) – (c).

The curves are almost the same between the blend and copolymer cases except the case

TE D

of model 1.

As seen in eqs 5, 10 and 15, the difference in Tom comes from the entropy difference of In all the cases, the entropy contribution of D…H

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the contribution of D…H pairs.

pairs becomes maximal at D molar content of 0.5, though the value is slightly different

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depending on the model.

As already discussed, the model 1 assumes the regular

side-by-side array of the same type of monomer sequences, and no consideration is made about the contribution of entropy term due to such a side-by-side arrangement. Among the various factors governing the melting entropy change (∆Sm), the vibrational

entropy term (Svib) seems to be significantly different, which must be estimated

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quantitatively by performing the lattice dynamical calculation for these different types

Conclusion

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of POM samples [29-32].

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The D/H molar fraction dependence of the equilibrium melting temperature Tom

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evaluated for the two types of D/H blend samples and D/H random copolymers was simulated on the basis of phenomenological treatments by assuming the statistical arrangements of the D and H units in the crystal lattice as well as along the chain axis. The

agreement

between

the

values

and

the

The blend samples between POM-H and POM-D

TE D

theoretically-estimated ones is good.

experimentally-evaluated

chains show rather higher Tom than the D/H copolymers, which originates from the The reasons of these differences

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difference in Tom(DH) or the difference in ∆Sm(DH).

are needed to be clarified from the microscopic point of view through the lattice

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dynamical treatments.

Acknowledgments

We thank Mr. Tomohiro Monma and Mr. Ken Horita of Polyplastics Co. Ltd., Japan for their kind support and discussion of the present study.

This study was

financially supported by a MEXT “the International Project on the Basic Research

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Promotion for the Development of Highly-Controlled Multi-Purpose Polymer Materials” in “the Strategic Project to Support the Formation of Research Bases at Private

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Universities” (2010 – 2014).

(1)

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References and Notes

A special issue on crystallization of polymers, Faraday Discuss. Chem. Soc.

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1979; 68. (2)

Ballard DGH, Wignall GD, Schelten J. Eur Polym J 1973; 9:965-969.

(3)

Schelten J, Wignall GD, Ballard DGH, Schmatz W. Coll Polym Sci 1974; 252:749-752.

Higgins JS, Benoit HC. Polymers and Neutron Scattering, Oxford University

TE D

(4)

Press, Oxford, 1993.

Schelten J, Wignall GD, Ballard DGH, Schmatz W. Polymer 1974; 15:682-685.

(6)

Schelten J, Ballard DGH, Wignall GD, Longmann GW, Schmatz W. Polymer

AC C

EP

(5)

1976; 17:751-757.

(7)

Schelten J, Wignall GD, Ballard DGH, Longman GW. Polymer 1977; 18:1111-1120.

(8)

Tashiro K, Stein RS, Hsu SL. Macromoelcuels 1992; 25:1801-1808.

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(9)

Tashiro K, Satkowaki MM, Li Y, Chu B, Hsu SL. Macromoelcuels 1992;

(10)

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25:1809-1815. Tashiro K, Izuchi M, Kobayashi M, Stein RS. Macromoelcuels 1994; 27:1221-1227.

Tashiro K, Izuchi M, Kobayashi M, Stein RS. Macromoelcuels 1994;

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(11)

(12)

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27:1228-1233.

Tashiro K, Izuchi M, Kobayashi M, Stein RS. Macromoelcuels 1994; 27:1234-1239.

(13)

Tashiro K, Izuchi M, Kaneuchi F, Jin C, Kabayashi M, Stein RS.

(14)

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Macromoelcuels 1994; 27:1240-1244.

Sasaki S, Tashiro K, Gose N, Imanishi K, Izuchi M, Kobayashi M, Imai M,

(15)

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Ohashi M, Yamaguchi Y, Ohoyama K. Polym. J. 1999; 31:677-686. Reddy KR, Tashiro K, Sakurai T, Yamaguchi N. Macromolecules 2008;

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41:9807–9813.

(16)

Reddy KR, Tashiro K, Sakurai T, Yamaguchi N. Macromolecules 2009; 42:1672–1678.

(17)

Reddy KR, Tashiro K, Sakurai T, Yamaguchi N, Sasaki S, Masunaga H, Takata M. Macromolecules 2009; 42:4191-4199.

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Krimm S, Ching JHC. Macromolecules 1972; 5:209-211.

(19)

Carven CJ, Hatton PD, Howard CJ, Pawley GS. J Chem Phys 1993;

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(18)

98:8236-8243. (20)

Wunderlich B. Macromolecular Physics, Vol. 3: Crystal Melting (Academic

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Press, New York, 1980).

Carter DR, Baer E. J Appl Phys 1966; 37:4060-4065.

(22)

Kongkhlang T, Reddy KR, Kitano T, Nishu T, Tashiro K. Polym. J. 2011; 43:66–

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(21)

73.

Hama H, Tashiro K. Polymer 2003; 44:2159–2168.

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Hama H, Tashiro K. Polymer 2003; 44:3107–3116.

(25)

Hama H, Tashiro K. Polymer 2003; 44:6973–6988.

(26)

Iguchi M, Murase T. Makromol Chem 1975; 176: 2113–2126.

(27)

Harwood H. J. Ritchey W. M. J Polym Sci Part-B Polym Lett 1964; 2: 601-607.

(28)

Strobl G. The Physics of Polymers Springer 1997.

(29)

Kobayashi M, Tadokoro H. Macromolecules 1975; 8:897-903.

(30)

Kobayashi M, Tadokoro H. J Chem Phys 1977; 66:1258-1265.

(31)

Trevino S, Boutin H. J Chem Phys 1966; 45:2700-2702.

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(32)

Sugeta H. Vibrational Spectra and Molecular Structures of Polyoxymethylene

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and Relatd Molecules, Dissertation, Osaka University, 1969.

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29

Table 1

POM Samples Used for the Experimental Evaluation of Tom

Mw

Mn

Ra

Mw/Mn

observed

D/H Copolymer

random

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Random

Copolymer model

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Sample

block

alternating

D29/H71

60400

26400

2.3

38%

42%

1%

60%

D48/H52

65400

27600

2.4

44%

50%

1%

100%

D69/H31

75300

29800

2.5

40%

42%

1%

60%

Delrin 100

198000

64400

3.1

Delrin 500

108000

39200

2.8

H100

52400

Duracon MI90 POM-D

172000

20000

2.6

72800

2.3

64800

2.7

R : run number: number of boundary between D and H monomer sequences [27]

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a

169000

TE D

POM-H

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Figures’ Caption (a) 13C NMR spectra measured for a series of D/H random copolymers of POM.

As shown in (b), the 5 peaks of

13

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Figure 1

C atom are furthermore

and HDH units (refer to the text).

Examples of the Gibbs-Thomson (GT) plots based on the crystallite

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Figure 2

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split to 3 sub-peaks, which correspond to the sequence of DDD, HDD

sizes detected by the SAXS method, where the data of POM-H homopolymers were compared. Figure 3

The D molar fraction dependence of the experimentally-estimated Tom The curves show the calculated results

TE D

of D/H random copolymers.

on the basis of the phenomenological equations derived in the text:

Figure 4

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solid line for model 2 and broken line for model 1 (refer to Figure 6). The D molar fraction dependence of the experimentally-estimated Tom

AC C

of the blend samples between POM-D and POM- H homopolymer (H100).

The curve shows the calculated result on the basis of the

phenomenological equations derived in the text.

Figure 5

The D molar fraction dependence of the experimentally-estimated Tom of the blend samples between POM-D and EO-POM copolymer

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(Duracon).

The curve shows the calculated result on the basis of the

Figure 6

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phenomenological equations derived in the text. Schematic illustrations of (a) the statistically-distributed POM-H and

POM-D chain stems in the crystalline lamella, (b) the hypothetical

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side-by-side arrays of the (D)n and (H)m segments of the POM

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copolymer chains (model 1), and (c) the statistically random distribution of (D)n and (H)m segments of POM copolymers in the crystalline lamella (model 2). Figure 7

The contribution of the entropy terms of the aggregated DD, HH and

TE D

HD segmental parts in (a) D/H random copolymers (models 1 and 2, respectively) and the blend samples of POM-D with (b) H100 and (c)

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EO-POM copolymer (Duracon).

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32

Figure 1

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33

Figure 2

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Figure 3

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35

Figure 4

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36

Figure 5

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(a) Blend

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POM-H (1-X)

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POM-D (X)

(b) Copolymer (model-1) Hm

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TE D

Dn

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(c) Copolymer (model-2) Hm

Dn

Figure 6

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38

Figure 7

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Highlights Random copolymers of deuterated and hydrogeneous oxymethylene monomer units




were synthesized for the first time. The equilibrium melting temperature has been evaluated for both D/H blends and




copolymers of POM experimentally. The phenomenological theory succeeded to reproduce these experimental data well.

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