액상 및 고상고분자물질의 상태식

류종화; 김종식

Polymer(Korea), Vol.17, No.5, 484-491, September, 1993

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액상 및 고상고분자물질의 상태식

The Equation of State for Liquid and Solid Polymers

류종화, 김종식

초록

자유공간 내에서 강체구처럼 진동하는 고분자 씨그먼트들의 점유체적에 대한 온도 및 압력의 영향은 무시될 수 있다는 가정에서 등온 체적탄성율을 표현하는 반 경험식을 얻었다. 이 등온 체적단성율 B_T=B₀[1+B(T)P]ⁿ을 적분하여 다음과 같은 상태식을 얻었다. ln(V/V₀)=n[B(T,P)-1]/(n-1)[2G_T(0)+5/3] 여기서 B₀는 P=0에서의 체적탄성율이고, n은 n≒1 정도의 상수이고, B(T)=[2G_T(0)+5/3](n. B₀), G_T(0)는 P=0에서의 등온 Gr neisen 인자이고, B(T, P)=(B₀/B_T)^1-1/n이다. 유도된 상태식의 상수들은 지금까지 보고된 선형 polyethylene(LPE), polystyrene(PS), poly(orthomethylsty-rene)(PoMS), poly(cyclohexyl methacrylate)(PCHMA), poly(methyl methacrylate) (PMMA), hexa-methyldisiloxane(HMDS) 및 여러가지 분자량의 poly(dimethylsiloxane)(PDMS)에 대한 비체적 측정치들을 이용 비선형 최소 자승법으고 구했다. 유도된 상태식으로 비체적치를 구해 문헌치, Tait의 상태식 및 Hartmann-Haque의 상태식으로부터 계산한 결과와 비교했다. 그리고 유도된 상태식을 이용하여 압축인자, 체적탄성율 및 Gr neisen 인자에 대한 온도 및 압력의 영향을 분석하고 문헌치들과 비교 검토했다.

A semiempirical expression about isothermal bulk modulus, BT. for Polymers is obtained on the supposition that the effects of temperature and pressure on the occupied volume of a polymer segment are negligible and the segment vibrates like a hard sphere in the free space which surrounds it. The isothermal bulk modulus, B_r=B₀[1+B(T)P]ⁿ, is integrated to give an equation of state, which is given by ln(V/V₀)=n[B(T,P)-1]/(n-1)[2G_T(0)+5/3] where B₀ is bulk modulus at P=0, n is a constant(n≒1), B(T)=[2G_T(0)+5/3]/(n B₀), G_T(0) is isothermal Gr neisen parameter at P=0 and B(T,P)=(B₀/B_r)^1-1/n. The parameters of the equation of state arre determinde by fitting this equation to the reported data about specific volume for linear polyethylene(LPE), polystyrene(PS), poly(orthomethyrene)(PoMS), poly(cyclohexyl methacrylate)(PCHMA), oily(methyl methacrylate)(PMMA), hexamethyldisiloxane(HMDS) and poly(dimethylsiloxane)(PMMA) of various molecular weight. For the above polymers, the predicted values of specific volume agree with the observed ones within hte accuracy of measurements, and the results clculaed from the equation of state are compared with those calculated from empirical Tait equation and semiempirical Hartmann-Haque equation. The effects of temperature and pressure in compressibilility, bulk modulus, and Gr neisen parameter are discussed on the basis of equation of state.

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[2] Sanchez IC, J. Appl. Phys., 45, 4204 (1974)

[3] Horrocks JK, McLaughlin E, Trans. Faraday Soc., 59, 1709 (1963)

[4] Kamal I, McLaughlin E, Trans. Faraday Soc., 60, 809 (1964)

[5] Barron RM, Barron THK, Mummery PM, Sharkey M, Can. J. Chem., 66, 718 (1988)

[6] Goodman MA, Whittenburg SC, J. Chem. Eng. Data, 28, 350 (1983)

[7] Goodman MA, Whittenburg SC, J. Chem. Eng. Data, 29, 125 (1984)

[8] Dugdale JS, MacDonald DKC, Phys. Rev., 89, 832 (1953)

[9] Warfield RW, Hartmann B, J. Appl. Phys., 44, 708 (1973)

[10] Mopsik FI, J. Chem. Phys., 50, 2559 (1969)

[11] Asay JR, Lamberson DL, Guenther AH, J. Appl. Phys., 40, 1768 (1969)

[12] Ito T, Marui H, Polym. J., 2, 768 (1971)

[13] Quach A, Simha R, J. Appl. Phys., 42, 4592 (1971)

[14] Olabishi O, Simha R, Macromolecules, 8, 206 (1975)

[15] Beret S, Prausnitz JM, Macromolecules, 8, 536 (1975)

[16] Lichtenthaler RN, Liu DD, Prausnitz JM, Macromolecules, 11, 192 (1978)

[17] Kubota K, Ogino K, Macromolecules, 11, 514 (1978)

[18] Hartmann B, Haque MA, J. Appl. Phys., 58, 2831 (1985)

[19] Shih H, Flory PJ, Macromolecules, 5, 758 (1972)

[20] Nakafuku C, Polymer, 19, 149 (1978)

[21] Boyer RF, Macromolecules, 14, 376 (1981)

[22] Wood LA, Polym. Lett., 2, 703 (1964)

[23] Hartmannn B, Haque MA, J. Appl. Polym. Sci., 30, 1553 (1985)

[24] Brostow W, Grindley T, Macip MA, Mater. Chem. Phys., 12, 37 (1985)

[25] Jain RK, Simha R, Macromolecules, 22, 464 (1989)

[26] Wu CK, Jura G, Shen M, J. Appl. Phys., 3, 4348 (1972)

[27] Wu CK, J. Polym. Sci. B: Polym. Phys., 13, 387 (1975)

[28] Barker RE, J. Appl. Phys., 38, 4234 (1967)

[29] Shen M, Polym. Eng. Sci., 19, 995 (1979)

[30] Leute U, Grossmann HP, Polymer, 22, 1335 (1981)

[31] Gilmour I, Trainor A, Haward RN, J. Polym. Sci. B: Polym. Phys., 16, 1291 (1978)

[32] Warfield RW, Makromol. Chem., 75, 3285 (1974)