# (218h) Measurement and Correlation of Solubility and Diffusion Coefficient of Ethylene in Molten Propylene-Co-Polymers

#### AIChE Annual Meeting

#### 2016

#### 2016 AIChE Annual Meeting

#### Engineering Sciences and Fundamentals

#### High Pressure Phase Equilibria and Modeling: Honoring Professor Cor J. Peters II

#### Monday, November 14, 2016 - 5:07pm to 5:23pm

Summary

Solubility

and diffusion coefficients of ethylene in molten poly(propylene-ethylene-1-butene)co-polymers

(PPs) with different crystallinities were measured at

140 Â°C and 180 Â°C and up to 2.5 MPa. There was no

significant difference in solubility of ethylene in PPs at each temperature. Experimental

solubility was successfully correlated by the Sanchez-Lacombe equation of state.

On the other hand, the diffusion coefficient of ethylene in PPs was not

identical. The difference of diffusion coefficient was possibly caused by the

difference of specific volume of the PPs and/or of glass transition temperature

of the PPs. Diffusion coefficient was successfully correlated by the Kulkarniâ??s Free-Volume-Theory.

IntroductionPropylene-co-polymer (co-PP) is widely used in the society due to its unique

mechanical and molding characteristics. In the industry, co-PP is usually

manufactured by the gas phase polymerization process which is progressed as

monomer molecules dissolve and diffuse into polymer and reach catalysts. Co-PP

is known as crystalline polymer having both crystalline and amorphous regions

in it and it has reported that monomer solution and diffusion only take place

in the amorphous region [1]. Therefore crystallinity

of co-PP strongly affects solubility and diffusivity of monomer in co-PP.

Furthermore, figuring out the relationship between crystallinity

and solubility and diffusivity of monomer is needed to optimize the

polymerization process. However, it is difficult to obtain phase equilibrium

data under a constant crystallinity since crystallinity has temperature and pressure dependences and

is changeable by thermal histories. Hence there have been reported only a few studies

that quantify the effect of crystallinity on

solubility and diffusivity of monomer in co-PPs with a wide range of crystallinity. In this work, solubility and diffusion

coefficient of ethylene in molten poly(propylene-ethylene-1-butene)co-polymers

(PPs) with different crystallinities were particularly

measured at 140 Â°C and 180 Â°C. The reason for the selection of temperature

above the melting point of PPs was to examine the affinity between ethylene and

PPs polymer chain without the effect of crystalline. In addition, solubility

and diffusion coefficient were correlated by the Sanchez-Lacombe equation of

state and the Kulkarniâ??s Free-Volume-Theory respectively.

Experiments

Ethylene was used as monomer and four poly(propylene-ethylene-1-butene)-co-polymers

with different crystallinities were used as polymer

samples. Characteristics of polymer samples are listed in Table 1. Melting

point was determined by DSC measurement and set as using peak top temperature. Crystallinity was determined by density. Measurement of

solubility and diffusion coefficient was operated by the gravimetric method

using a Magnetic Suspension Balance (MSB) under 140 °C and 180 °C and up to 2.5

MPa with 0.5 MPa steps.

Table 1 The

Characteristics of PPs

Models

Solubility of ethylene in PPs was correlated by the Sanchez-Lacombe

equation of state (SL-EoS) [3, 4] shown in Equations

1 and 2.

(1)

(2)Where

*P**, *r**, and *T** are characteristic parameters of the SL-EoS.

The characteristic parameter of ethylene and PPs were referred by Satoâ??s

experiment [5, 6] as assuming that the characteristic parameters of homo-polypropylene

can be used to the ones of PPs used in this work. In order to apply the SL-EoS to binary systems, the mixing rule expressed in

Equation 3 was used with binary interaction parameter *k*_{ij} as follows,

(3)

Where

*k*_{ij}

was a fitting parameter for correlation.

On the other hand, diffusion coefficient was correlated by the Kulkarniâ??s Free-Volume-Thoery (FVT)

[7] expressed in Equations 4, 5 and 6.

(4)

(5)

(6)Where

*A _{d}*,

*B*and

_{d}*g*are

fitting parameters of the FVT and determined for each ethylene/PP system as

temperature independent parameters. The chemical potential of monomer in PPs,

*m*

_{1}

^{P},

expressed in Equation 4 was determined by the SL-EoS.

The thermal expansion coefficient,

*a*, and

the compressibility coefficient,

*b*,

were evaluated by the method which Kulkarni

*et al*. [7] suggested with the data of

PVT measurement. The standard free volume fraction of polymer,

*v*

_{fs},

expressed in Equation 6 was referred by the universal value suggested by Wiliams et al [8].

Results and Discussions

Figures 1 and 2 show the solubilities of ethylene

in PPs at 140 °C and 180 °C, respectively. The solubilities

increased with decreasing temperature and increasing pressure linearly. Solid

lines in Figures 1 and 2 denote the correlation by the SL-EoS.

Experimental solubility of ethylene in PPs was successfully correlated with the

SL-EoS within the AAD defined by Equation 7 of 0.7%.

Moreover, solubility of ethylene in four different PP samples showed almost similar

values and the deviation of solubility in PP1 and PP4 defined by Equation 8 was

2.8% in 140 °C and 1.4% in 180 °C. Figure 3 shows the temperature dependence of

*k*_{ij},

the binary interaction parameter in the SL-EoS in the

series of correlation. The maximum deviation of *k*_{ij} of PPs at both

temperatures was 9.6% in 140 Â°C, which changes solubility less than 3%. Hence, *k*_{ij}

can be treated as a constant for all PPs at each temperature.

Figure

1 Solubility of ethylene in PPs at 140 Â°C

Figure

2 Solubility of ethylene in PPs at 180 Â°C

Figure

3 Temperature dependence of *k*_{ij} in

SL-EoS

Figures

4 and 5 show the diffusion coefficients of ethylene in PPs at 140 Â°C and 180 Â°C,

respectively. Diffusion coefficients of ethylene in PPs increased with

increasing temperature and concentration of ethylene. Solid lines in Figures 4

and 5 are the results of correlation by the FVT. Experimental diffusion

coefficients were successfully correlated with the FVT within the AAD defined

in Equation 9 of 4.0% at both temperatures. Additionally, the deviation of

diffusion coefficients of ethylene in PP1 and PP4 derived by Equation 10 was

about 22% in both temperatures. So it can be noticed that diffusion coefficients

of ethylene in PP4 is systematically larger than in PP1, while there wasnâ??t a

significant difference in the solubility.

(9)

(10)Figure 6

shows the relationship of diffusion coefficients at infinite dilution and free

volume fraction of PPs. The diffusion coefficients at infinite dilution were

calculated by extrapolating the FVT to zero concentration. Free volume

fractions of PPs were derived by PVT measurement. It can be seen in Figure 6

that the diffusion coefficients at infinite dilution of PP1 and PP4 at the same

value of free volume fraction were almost equal and ones of PP2 and PP3 were

lower than of PP1 and PP4.

Figure 4 Diffusion

coefficient of ethylene in PPs at 140 Â°C

Figure

5 Diffusion coefficients of ethylene in

PPs at 180 Â°C

Figure

6 Diffusion coefficient vs free volume fraction of PPs at infinite dilusion

Conclusion

The solubilities and diffusion coefficients of ethylene in molten

PPs were measured at 140 Â°C and 180 Â°C and up to 2.5 MPa.

Both experimental solubilities and diffusion

coefficients were correlated by the SL-EoS and the

FVT, respectively. It can also be noted that the free volume fraction of PPs might

be the key parameters for relating the solubility and diffusion of ethylene in

polymers. Hence the PVT measurement of PPs would lead better understandings of

the relationship between the diffusion coefficients and the specific volumes of

PPs.

References

[1] A.S. Micheals and H. Bixler,

*J. Polym. Sci., 50, 413 (1961).* [2] I.C.

Sanchez and R.H. Lacombe,

*J. Phys. Chem*.,

**80**, 2353 (1976). [3] I.C. Sanchez and R.H. Lacombe,

*Macromolecules*,

**11**, 1145

(1978). [4] Y. Sato, M. Yurugi, T. Yamabiki, S. Takishima and H. Masuoka,

*J. Appl. Polym. Sci.,*

[5]

**79**, 1134 (2001).Y. Sato, A. Tsuboi, A. Sorakubo,

S. Takishima, H. Masuoka,

T. Ishikawa,

*Fluid Phase Equilibria*,

**170**,

49 (2000). [6] S.S. Kulkarni and S.A. Stern,

*Journal of Polymer Science: Polymer Physics*

Edition,

Edition

**21**, 441 (1983). [7]

M.L. Williams, R.F. Landel, and J.D. Ferry,

*J. Am. Chem. Soc*.,

**77**, 3701 (1955).

Symbols*P* [MPa]:

pressure,

*r* [kg/m^{3}]: density, *T* [K]: temperature, *P*^{*} [MPa], *r*^{*}

[kg/m^{3}], *T*^{*}

[K]: characteristic parameters in the SL-EoS, *r* [-]: number of segment, *f* [-]:

volume fraction, *k*_{ij}

[-]: interaction parameter, *D*_{mutual} [m^{2}/s]: mutual diffusion

coefficient, *D*_{self}

[m^{2}/s]: self diffusion coefficient, *x* [-]: mole fraction, *R* [J/mol/K]:

gas constant, *m*^{P} [J/mol]: chemical potential of polymer, *A*_{d} [m^{2}mol/(s J)], *B*_{d}

[-], *g* [-]:

characteristic parameters, *T*_{g} [K]: glass transition temperature of polymer, *a* [K^{-1}]:

thermal expansion coefficient, *b* [MPa^{-1}]:

compressibility coefficient, *v*_{f} [-]: free volume fraction of polymer, *v*_{fs}

[-]: free volume fraction of polymer at standard state, *v*_{f}_{,â??} [-]:

free volume fraction of polymer at infinite dilution, *Sol* [g_gas/g_polymer]:

solubility, *D* [m^{2}/s]:

diffusion coefficient

Index

1: monomer, 2: polymer, s: standard state

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