Journal, Vol. 4, No. 3, pp 316-322 (1973)

Lower Critical in Linear -n- Systems

Fumiyuki HAMADA, Koichi FUJISAWA, and Akio NAKAJIMA

Departmement of Polymer , Kyoto University, Sakyo-ku, Kyoto, Japan. (Received June 8, 1972)

ABSTRACT: The molecular dependence of the lower critical solution tem­ perature (LCST) of linear polyethylene in n-C5H12, n-CGH14, n-C7H16 and n-CsH1s was determined and theta temperature <9L was obtained according to Shultz-Flory's equation. Observed values of Eh were compared with the values calculated by using equation-of­ state parametes based on the theories on developed by Flory and Patterson. KEY WORDS Lower Critical Solution Temperature / Polyethylene Normal Alkane / x Parameter / Equation of State /

It is common that the mutual of a Conventional theory of polymer solution by non-polar polymer with a polar or other poor Flory-Huggins12 failed to explain this LCST but increases with increasing temperature the new thermodynamic theories on polymer solu­ until complete is reached at an upper tions developed by Flory9 •13 ·14 and Patterson17 ·18 critical solution temperature (UCST). There are, can explain very well the new LCST phenomenon however, a few systems composed of a polar as discussed later. polymer and a polar solvent for which the mutual The value of LCST is dependent on the solubility increases with decreasing temperature molecular weight of and decreases with and in which complete miscibility is attained increasing molecular weight, in contrast to the at a lower critical solution temperature (LCST). case of UCST. From the molecular weight These are, almost without exception, aqueous dependence of LCST we can obtain the theta solution of a polar polymer, such as poly( temperature eL 8 by extraporating the values of ),1 poly(propylene oxide),1 partly acetylated LCST at various molecular to infinite poly(vinyl ), 2'3 partly formalized poly­ molecular weight, in the same manner as to ob­ (vinyl alcohol),2'3 methyl ,4 and poly­ tain the theta temperature Bu from UCST.12 (vinyl methyl ). 5 Such a LCST is found Two of the authors8 (A. N. and F. H.) have only for in which both components are determined the molecular weight dependence of highly polar, and is usually below the boiling LCST for linear polyethylene fractions in n­ temperature of the solvent. Another type of , and n- and obtained eL 8 • In solution which shows a LCST was found for this paper, we have further determined the systems composed of a non-polar polymer and molecular weight dependence of LCST for a non-polar solvent, 11 for example, ­ linear polyethylene fractions in n- and ,6 polyisobutylene-n-pentane, 7 and poly­ n- and will discuss the observed values of ethylene-n-alkane. s-ll 'J'he LCST of these sys­ eL for polyethylene in n- in connection tems is usually found at higher temperature than with the number of n-alkanes. We have the boiling temperature of the solvent and, more­ carried out some calculations to obtain eL of over, negative heat of mixing is found near the polyethylene in n-alkanes from theoretical con­ LCST. The latter LCST has rather recently been siderations basically developed by Flory and noticed because it lies above the boiling tempera­ Patterson. Thus observed values of (9L are ture of the solvent, but seems to be a completely compared with calculated ones. general phenomenon for polymer solutions.

316 Lower Critical Solution Temperature


Sample A linear polyethylene Sholex 6009 (polyethylene of Marlex 50 type, manufactured by Japan Olefin Chem. Co.) was fractionated into 10 fractions in a column designed by us.19 The polymer percipitated on Celite (No. 545) by cooling from where

C6H14 and n-C7H 16 were spectrograde reagents. of segment of solvent and solution, respectively, These solvents were used without further puri­ P= * is the characteristic p* of n-alkane fication. with infinite number of carbon and b' is assumed as constant for all n-alknanes. Measurements of Precipitation Temperature The series expansion of the chemical potential Each of the polymer fractions with different given by eq 2 can be written as molecular weights was sealed in a small glass tube, under nitogen, together with solvent con­ taining 10 ppm of 2, 6-di-tert-butyl-p-cresol. The µl;;i° -( :: )

Polymer J., Vol. 4, No. 3, 1973 317 F. HAMADA, K. FUJISAWA, and A. NAKAJIMA

Also x may be expressed by a series in powers expressed by neglecting higher terms of solute of segment fraction cp 2 • concentration by the following equation, x=Xi+X2

Therefore, from eq 8 and 9, we have Where ,r;1 and ¢1 are heat and parameter such that l1H =RT,r; v/ =(J_)[3x c ( l + 2X1P12] (10) 1 1 Xi 2 i i -f4- Ty T- l _ _JJ__i_ V 1 l1S1=R¢1V22 (15) T/ If we assume that the theta temperature (9 is The first term in the right hand side of eq 10 expressed by is an equation-of-state term (free volume term) and increases with increasing temperature while (16) the second term is the contact energy term we can get and decreases with increasing temperature. We confine present consideration to -liquid (17) miscibility. From the condition for critical miscibility, From eq 14, 17, and 12, we have

( ~) -0 -¢1(1- ~)=Xie-~ =X-1/2+ 21X (18) O

where x is the ratio of the molar volumes of 150 .------, polymer and solvent. Since critical concentra­ tion, however, occurs at a very small of polymer12 , Xe is nearly equal to Xie, which is Xi at critical temperature. Therefore 140 from eq 10 and 11, we have M•4,900

2 3X1C1 ( 1- -T 1*- ) 13Q ~-~--T.~2_* + 2X1P12 (12) 1- 4v1Tc Tevi T/ ... I- This equation shows the dependence of the 120 critical solution temperature on the molecular weight of polymer. For infinite x, we can get 110 ~60 M•l4,300

100 ______. This equation immediately predicts the occur­ 0 0,05 0.10 rence of BL in the of n-alkane with Va polyethylene. With complete generality, the Figure 1. Phase diagrams for polyethylene frac­ excess chemical potential of solvent may be tions in n-pentane.

318 Polymer J., Vol. 4, No. 3, 1973 Lower Critical Solution Temperature

231 ~------,

160-~ ~o t.1•34,900 228 M=93500

u M=125000 150 -V.1.200 225 V .,,o,ooo

2220 V 0.05 2 Figure 4. Phase diagrams for polyethylene frac­ 140 L-,.____ .______, tions in n-octane. 0 0-05 0,10 Vz Figure 2. Phase diagrams for polyethylene frac­ tions in n-pentane.

192~------, 2.7

" ; M=76800 2.5 189 M=93500 "'0 X u 1-'-' . :::, ~M=l25000 2.3


2.1 J M•202000 y2 0.05 Figure 3. Phase diagarms for polyethylene frac­ 1.9 o____ _._ ____...... ______. tions in n-heptane. 201xt+ l/2Xl 102 6 Figure 5. Plots of the reciprocal critical tempera­ of temperature we can get fJ and ¢ 1 from the ture against the molecular size function for poly­

plot of reciprocals of T0 against the function ethylene fractions in n-pentane, n-hexane, n• x- 112 + I/2x according to Shultz-Flory method. heptane, and n-octane. Thermodynamic theory of polymer solutions using the equation-of-state parameter shows that not strictly correct. In this paper, however, we 15 16 generally ¢ 1 is dependent on temperature • , obtained experimentally theta temperature by and eq 16 is not valid. Therefore theta tem­ Shultz-Flory method and the observed values perature, fJ obtained by Shultz-Flory method is of fJ was compared with the values calculated

Polymer J., Vol. 4, No. 3, 1973 319 F. HAMADA, K. FUJISAWA, and A. NAKAJIMA by eq 13. signs and, moreover, are nearly equal independent Precipitation temperature Tv for polyethylene of the number of carbon in the n-alkane, at fractions in n-C5H 12 , n-C6H 14 , n-C7H 16 , and n• least from n-C 6H12 to n-CsH1s· C8H18 is plotted against the volume fraction v2 The calculated values of (9L of polyethylene­ of polymer in Figures 1, 2, 3, and 4, respec­ n-alkane systems by eq 13 were shown on first tively. LCST decreases with increasing molecular line of Table II. Numerical calculations have weight of polyethylene in contrast to the case been carried out using the equation-of-state of UCST. Critical volume fraction decreases parameter shown in Table III with b' =0.40 and with increasing molecular weight in similar way x1=n+ 113 , where n is the number of carbon with the case of UCST. atoms of n-alkane. These equation-of-state pa­ The plot of reciprocals of the lower critical rameters were taken from the experimental solution temperature, T 0 obtained from these values by Orwall and Flory9 and selected data curves against the function x-112 +1/2x is shown from the literature.21 The thermal pressure co­ in Figure 5, from which the theta temperature (9L, efficient, r of n-C8H 18 at theta temperature was and entropy parameter ¢1 were determined. obtained by extraporating the value of r of n• These were shown in Table I together with the C8H18 in 21 ° -150°C to theta temperature. Since ,c (9L enthalpy parameter 1 at 130°C. increases values of n-C5H 12 and n-C7H 16 at theta temper­ with increasing the number of carbon atoms in ature were not available in literature and it the n-alkane. Both ¢1 and ,c1 show negative was not possible to calculate the theta temper­

ature of n-C6H 12 and n-C7H 12 by eq 13. Param­ Table I. Experimental values of Eh, ¢1, and ,c1 eter (3 12 for polyethylene-n-alkane systems was for polyethylene-n-alkane systems shown on the second line of Table II. Calcu­ lated values of (9L agree with experimental value of (9L rather well. €h, °C ca. 80 133.3 173.9 210.0 Patterson22 also has shown that (9L can be 'fl -1.3 -1.0 -1.2 -1.1 calculated by eq 20 together with the reduced /Cl at 130°C -1.1 -1.0 -1.1 -1.0 equation-of-state of eq 21. Table II. Calculated values of Eh for l+Ci'r2(l+x-112 2-fV1-113 p--2 l\ r (20) polyethylene-n-alkane systems 1-Cir\1 +x-112)-2-i V1- 113 n-CsH1s 1'1 =(F1 P-1 + P-1- 1)(1- P-1 - 113) (21) €h, °C (from eq 13) 133.0 215.4 where P-1 is the reduced volume per mole of /312, °K 6.58 3.82 solvent, C1 is the number of external degrees of (9L, °C (from eq 20) 164.2 230.3 freedom of solvent and r is defined by

Table III. Equation-of-state parameters used in calculating BL from eq 13 (a) n-alkane9,21

Vsp, ax 103, r, v*, T*, P* , fc, °C cc g-1 deg-1 cal cc-1deg- 1 v ccmol-1 OK cal cc-1 XC CsH14 133.0 1.84019 2.30319 0.08649 1.5651 14.454 4579 85.53 0.9511 CsH1s 215.4 1.954719 2.63019 0.0624 1.6745 14.798 5183 85.47 1.1052

(b) Polyethylene9

ax 103, r, T*, P*, fc, °C deg-1 cal cc-1deg- 1 v OK cal cc-1 133.0 0. 718 0.177 1.2430 7212 110.80 215.4 0.768 0.126 1.2983 7612 103.95

320 Polymer J., Vol. 4, No. 3, 1973 Lower Critical Solution Temperature

Table IV. Equation-of-state parameters used in calculating Eh from eq 20 (a) n-alkane9,21

'Vsp, ax103 r, v*, T* P* Liquids fc, °C cc g-1 deg-1 cal cc-1deg- 1 v ccmol-1 OK' cal cc-' 1 C

CsH14 164.2 I. 995619 3.01819 0.06149 1.6832 14.577 4614 76.01 0.8459 CsH1s 230.3 2.0331 19 2.92319 0.0578 I. 7209 14.976 5227 86.12 1.1176

(b) Polyethylene9

ax 103, T* fc, °C deg-1 v OK' 164.2 0.727 1.2608 7406 230.3 0.785 1.3104 7646

between J\ and 1'1 and the extraporation of T to P=0 yields fh. As an example, the relation between f\ and T'1 for polyethylene with n­ hexane is shown in Figure 6 and that between P and T is shown in Figure 7, from which we can obtain /Eh. These values obtained for th are shown on the forth line of Table II. The equation-of-state parameters used in this calcu­ 0.02 lation are shown in Table IV. These equation­ of-state parameters were taken from experimental values by Orwall and Flory9 and selected data

from the literature.21 Since r values of n-C5H 12 not avail­ 0 and n-C7H 16 at theta temperature were 0.lf 0.14 able in literature and it was not possible to calculate thata temperature of n-C5H 12 and n­ Figure 6. Plot of P against T for polyethylene in C7H12 by eq 20 and 21. n-hexane. As shown in Table II, the value of Eh cal­ method is considerably 200,------, culated by Patterson's larger than that of observed Eh. Such results may be well explained in the following way. 150 Evidently from procedure above mentioned, e /Eh calculated by Patterson's method corresponds ~100 to temperature which satisfies a following equa­ Q. tion. 50 (23) We can derive eq 23 from Flory's equation 13

530T(oK) 630 with /3 12 =0 and together with the reduced equa­ tion of state (eq 21) at P=0. If the second Figure 7. Plot of P against T for polyethylene in term of the left hand side in eq 13 is neglected, n-hexane. the calculated value of fh becomes larger. T/ Therefore the disagreement of value of Eh cal­ ,=l---*• (22) culated by Patterson's method with observed T2 value of fh with decreasing number of carbon From eq 20 and 21, we can derive a relation of n-alkane is obvious considering that

Polymer J., Vol. 4, No. 3, 1973 321 F. HAMADA, K. FUJISAWA, and A. NAKAJIMA

we can't neglect {3 12 because of the end effect 3, 215 (1962). of the n-alkane with a small number of carbon 8. A. Nakajima and F. Hamada, Rep. Progr. atoms. Polym. Phys. Japan, 9, 41 (1966). We obtained Eh by Shultz-Flory's methods 9. R. A. Orwall and P. J. Flory, J. Amer. Chem. Soc., 89, 6814 (1967). as mentioned above, but eL should be obtained 10. D. Patterson, G. Delmas, and T. Somcynsky, by considering equation-of-state term. Also it Polymer, 8, 503 (1967). ¢ and must be noted that entropy parameter 1 11. P. I. Freeman and J. S. Rawlinson, ibid., 1, enthalpy parameter ,c1 obained by Shultz-Flory's 20 (1960). method are higher than those obtained by 12. P. J. Flory, "Principle of ," measurement on dilute solu­ Cornell University Press, New York, N. Y., tions12. These factors will be discussed in a 1953. subsequent publication. 13. P. J. Flory, R. A. Orwall and A. Vrij, J. Amer. Chem. Soc., 86, 3507 and 3515 (1964). REFERENCES 14. P. J. Flory, J. Amer. Chem. Soc., 87, 1833 (1965). 15. B. E. Eichinger, J. Chem. Phys. 53, 561 (1970). 1. G. N. Malcolm and J. S. Rawlinson, Trans. 16. B. E. Eichinger and P. J. Flory, Trans. Faraday Faraday Soc., 53, 921 (1957). Soc., 64, 2035 (1968). 2. F. F. Nord, N. Bier, and S. N. Timasheff, J. 17. G. Delmas, D. Patterson, and T. Somcynsky, Amer. Chem. Soc., 73, 289 (1951). J. Polym. Sci., 52, 79 (1962). 3. I. Sakurada, Y. Sakaguchi, and N. Ito, Kobunshi 18. D. Patterson, , 2, 672 (1969). Kagaku (Chem. High Polymers, Japan), 14, 41 19. S. Hayashi, F. Hamada, A. Saijo, and A. Naka­ (1957); Y. Sakuguchi, and N. Ito, Ibid., 15, 635 jima, Kobunshi Kagaku (Chem. High Polymers, (1958). Japan), 24, 769 (1967). 4. K. Uda and G. Meyerhoff, Macromol. Chem., 20. R. Chiang, J. Phys. Chem., 69, 1645 (1965). 47, 168 (1961). 21. S. Young, recorded by J. Timmermans, 5. C. E. Shildknecht "Vinyl and Related Poly­ "Physico-Chemical Constants of Pure Organic mers," Willy, New York, N. Y., 1952. Constants", Vol. 1, Elsevier Publishing Co., 6. H. Tampa, J. Polym. Sci., 8, 51 (1952). New York, N. Y., 1968. 7. C.H. Baker, W. B. Brown, G. Gee, J. S. Raw­ 22. D. Patterson and G. Delmas, Trans. Faraday linson, D. Stubley, and R. E. Yeadon, Polymer, Soc., 65, 708 (1968).

322 Polymer J., Vol. 4, No. 3, 1973