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On the relationship between wetting and adsorption of polymeric resins
Short Communication On the relationship between wetting and adsorption of polymeric resins Chuncai Yao, Shaofu Shari**and Chi Tien Department of Chemical Engineering Syracuse, NY, USA
and Materials Science,
Syracuse
University,
A general relationship between wetting and adsorption of polymeric resins is derived from the Gibbs and Young’s equations and its implications discussed.
Keywords: adsorption; wetting; polymeric resins; organics
Several investigators’-4 in recent years have reported results on the adsorption of organics from aqueous solution with hydrophobic resins (e.g., Amberlite XAD-4). These results demonstrate that wetting of adsorbents (resins) by an aqueous solution is determined by the surface tension of the solution and the contact angle between the solution and the surface of the adsorbent. The extent of the wetting, in turn, affects the adsorption behavior of the resin. Specifically, the adsorption capacity of the resin varies depending on whether the resin is prewetted or not. In an effort to explain the observed effect of wetting on adsorption, Rixey and King’ proposed a simple relationship, based on thermodynamic considerations, expressing the ratio of the adsorption density at the solid-liquid interface to that at the solid-vapor interface as a function of the surface tension and contact angle. The purpose of this article is to present a general relationship between wetting and adsorption and to examine its implications. It will be shown that this general relationship reduces to that of Rixey and King under certain conditions. We begin with the Gibbs isotherm equation at the liquid-vapor interface5: -da’”
= r’,“d/q
+ I’&“dp,
Address reprint requests to Dr. Yao at the Department of Chemical Engineering and Materials Science, Syracuse University, Syracuse, NY 13244, USA. *Present address: Nanjing Forestry University, Nanjing, China. Received 20 November 1990; accepted 10 February 1991
Separations
Technology,
-d&
= I’Fdp,
= RTT:“d(lna2)
(2)
where R is the gas constant, T the temperature, the activity of the solute. Similarly, at the solid-liquid interface
and a2
-da”‘=RTTfd(lna,)
(3)
and at the solid-vapor interface -du”“=
RTTyd(lna,)
(4)
where the vapor is in equilibrium with the liquid solution. From Equations 3 and 4 one obtains d(as” - &‘) dUna,)
= RT(Tt
which, on the substitution
- I’?)
(5)
of the Young’s equation
o=J - &I = &J cos 0
(6)
gives
(1)
where & is the liquid-vapor interfacial tension, It and I? are, respectively, the surface excesses (mass
282
per unit inter-facial area) of components 1 (solvent) and 2 (solute), and pI and E.C, are the corresponding chemical potentials. By choosing the Gibbs dividing surface such that I’$ = 0 9 one then has
1991, vol. 1
(7)
Combining Equations 2 and 7, one gets d(v~~cos~) = rr da’”
- rf
(8)
rf
For the special case where If I’?, Equation 8 becomes 0
is nearly equal to
1991 Butterworth-Heinemann
Wetting and adsorption of polymeric resins: C. Yao, S. Shan and C. Tien dcr’”cos8 ry da[” =-E-l=?1
(9)
where r = I’y/I’;l. If the assumption is made that r is independent of the surface tension or the concentration of the solution, then Equation 9 can be integrated to give u~“cose - a$cose,
= (r - l)(@
- C?)
(10)
where the subscript u denotes the pure solvent. It can be easily shown that the application of Equation 10 to the wet point gives Equation 12 of Rixey and King.’ To see the implications of Equation 7, we rewrite it as d(a” case) dcz
dc,
= RT(r$
dUna,)
- ry)
(11)
where c2 is the solute concentration of the solution. Since the activity of a component generally increases with its concentration, Equation 11 implies that r;’ - rs,Uhas the same sign as d(a’” cosO/dc,. In other words, whether the surface excess at the solid-liquid interface is larger or smaller than that at the solid-vapor interface depends on whether u’” cos/3 increases or decreases with the solute concentration. Since there are standard methods6 of estimating the surface tension and the activity of a binary solution, a measurement of 8 or (T[”CO&Jas a function of the solute concentration would enable one to estimate r $’ - r “2”from Equation 11. One way of measuring u lU case is by performing the capillary flow experiments, in which the advancing of the liquid solution is a function of time in a capillary made of the solid material of interest. u’” cosf3 is then calculated from the Washburn equation’: ,lv
cos(j
=
z!&T Rt
other means. In other words, Equation 11 provides a possible way of verifying experimentally the Gibbs or Young’s equation. The surface excesses I’;’ and r? can be obtained experimentally. First, it should be noted that I’sr and rs,U in Equation 11 are defined such that r ;’ = 0 and ry = 0.Since experimental measurements are often made based on unit mass of the solid material, we write r2as r2 = ?jZ
(13)
s
where A, is the specific surface area of the solid and 7r2 is the surface excess amount per unit mass of the solid. The relationship between ~~ and the actual adsorbed amount is derived as follows. Suppose that on unit mass of the solid the individual adsorbed amounts are IZ~and n2, respectively, for components 1 and 2. Then imagine a (Gibbs) dividing surface that divides the total adsorbed amount n, + n2 into two parts: part 1 consists of the solute surface excess r2 (which is pure solute), and part 2 is the difference (nl + n2) - 7r2.The concentrations of components 1 and 2 in part 2 are defined to be, respectively, c,/(c, + c2) and c2/(c, + c2), where cl and c2 are, respectively, the concentrations of components 1 and 2 in the equilibrium bulk phase. Then a mass balance for the solute gives n, = (nl + n2 - 7r2)~ c2 +?7 2 Cl + c2
(14)
7~~= n2 - n, 22 cl
(15)
or
of 7r2reduces to that of n, and
Thus, the measurement
(12)
where L is the length of the liquid column at time, t, R is the radius of the capillary, and 77is the viscosity of the liquid solution. Once r$ - I’;U has been estimated, one may proceed further with more assumptions. For example, if it is assumed that r$ is nearly equal to rk, which can be calculated from Equation 2, then rp can be estimated. Another possibility is that in some cases I’$ is much greater than r;v and thus the value of I’$ - ry can be taken as an estimate of I’$. The previous discussions show that the adsorption behavior of a solid material can be qualitatively assessed through contact angle measurements or capillary flow experiments. Since all the quantities in Equation 11 can (in principle at least) be measured, its validity can thus be verified experimentally. Because Equation 11 is derived from the Gibbs equation and the Young’s equation, once the validity of Equation 11 is established the validity of the Gibbs equation (or the Young’s equation) would follow if the validity of the Young’s equation (or the Gibbs equation) is assumed or established by some
122.
Equation 15 is convenient to use in solid-vapor adsorption where the individual adsorbed amounts are often measured. But for solid-liquid adsorption, batch experiments are often performed where the reduction of the solute concentration in the bulk phase before and after adsorption equilibrium is observed. In this case, we derive another equation for 7~~as follows. Suppose that in a batch experiment, unit mass of the solid is mixed with n, amount of solution of solute concentration c~~.After adsorption equilibrium the solute concentration of the solution reduces to c2. Then a mass balance for the solute gives n, = (c20n0 - nl -
n2k2
+
n2
(16)
or c2=
no(c20
-
~2)
(17) 1 - c2 Since 1 - c2 = cl for a binary solution, from Equations 15 and 17 one obtains n2 -
4
= =
n&20
2
1 -
c2
-
~2)
(18)
1 - c2
Separations
Technology,
1991, vol. 1
283
Wetting and adsorption
of polymeric
resins: C. Yao, S. Shan and C. Tien
Finally, we would like to note that when a porous adsorbent is in contact with a liquid, true solid-liquid adsorption does not always take place. It is possible that (some) pores of the adsorbent are not invaded (or fully wetted) by the liquid, and thus in these pores solid-vapor adsorption takes place. Such is the case when hydrophobic resins (e.g., Amberlite XAD-4) are in contact with dilute aaueous solutions of oreanits. To obtain true solid-liquid adsorption isotherms for these resins, the common practice is to prewet them.
284
Separations
Technology,
1991, vol. 1
References 1. 2 ’ 3.
z: 6.
7.
Rixey, W.G. and Ring, C.J. J. Colloid Interface Sci. 1989,131, 320 Rixey, W.G. Nonwet adsorbents for the selective recovery of polar organic solvents from dilute aqueous solutions. Ph.D. thesis, 1987. University of California, Berkeley, CA, USA Yao, C. and Tien, C. AZChE J. 1989,35, 1559 Yao, C. and Tien, C. Reactive Polymers 1990, l3, 121 Adamson, A.W. Physical Chemistry of Surfaces. New York: John Wiley & Sons, 1976 Reid, RC:, Prausnitz, J.M. and Poling, B.E. The Properties of Gases and Liquids. New York: McGraw-Hill, 1987 Fisher, L.R. and Lark, P.D. J. Colloid Interface Sci. 1979,69, 486
and Materials Science,
Syracuse
University,
A general relationship between wetting and adsorption of polymeric resins is derived from the Gibbs and Young’s equations and its implications discussed.
Keywords: adsorption; wetting; polymeric resins; organics
Several investigators’-4 in recent years have reported results on the adsorption of organics from aqueous solution with hydrophobic resins (e.g., Amberlite XAD-4). These results demonstrate that wetting of adsorbents (resins) by an aqueous solution is determined by the surface tension of the solution and the contact angle between the solution and the surface of the adsorbent. The extent of the wetting, in turn, affects the adsorption behavior of the resin. Specifically, the adsorption capacity of the resin varies depending on whether the resin is prewetted or not. In an effort to explain the observed effect of wetting on adsorption, Rixey and King’ proposed a simple relationship, based on thermodynamic considerations, expressing the ratio of the adsorption density at the solid-liquid interface to that at the solid-vapor interface as a function of the surface tension and contact angle. The purpose of this article is to present a general relationship between wetting and adsorption and to examine its implications. It will be shown that this general relationship reduces to that of Rixey and King under certain conditions. We begin with the Gibbs isotherm equation at the liquid-vapor interface5: -da’”
= r’,“d/q
+ I’&“dp,
Address reprint requests to Dr. Yao at the Department of Chemical Engineering and Materials Science, Syracuse University, Syracuse, NY 13244, USA. *Present address: Nanjing Forestry University, Nanjing, China. Received 20 November 1990; accepted 10 February 1991
Separations
Technology,
-d&
= I’Fdp,
= RTT:“d(lna2)
(2)
where R is the gas constant, T the temperature, the activity of the solute. Similarly, at the solid-liquid interface
and a2
-da”‘=RTTfd(lna,)
(3)
and at the solid-vapor interface -du”“=
RTTyd(lna,)
(4)
where the vapor is in equilibrium with the liquid solution. From Equations 3 and 4 one obtains d(as” - &‘) dUna,)
= RT(Tt
which, on the substitution
- I’?)
(5)
of the Young’s equation
o=J - &I = &J cos 0
(6)
gives
(1)
where & is the liquid-vapor interfacial tension, It and I? are, respectively, the surface excesses (mass
282
per unit inter-facial area) of components 1 (solvent) and 2 (solute), and pI and E.C, are the corresponding chemical potentials. By choosing the Gibbs dividing surface such that I’$ = 0 9 one then has
1991, vol. 1
(7)
Combining Equations 2 and 7, one gets d(v~~cos~) = rr da’”
- rf
(8)
rf
For the special case where If I’?, Equation 8 becomes 0
is nearly equal to
1991 Butterworth-Heinemann
Wetting and adsorption of polymeric resins: C. Yao, S. Shan and C. Tien dcr’”cos8 ry da[” =-E-l=?1
(9)
where r = I’y/I’;l. If the assumption is made that r is independent of the surface tension or the concentration of the solution, then Equation 9 can be integrated to give u~“cose - a$cose,
= (r - l)(@
- C?)
(10)
where the subscript u denotes the pure solvent. It can be easily shown that the application of Equation 10 to the wet point gives Equation 12 of Rixey and King.’ To see the implications of Equation 7, we rewrite it as d(a” case) dcz
dc,
= RT(r$
dUna,)
- ry)
(11)
where c2 is the solute concentration of the solution. Since the activity of a component generally increases with its concentration, Equation 11 implies that r;’ - rs,Uhas the same sign as d(a’” cosO/dc,. In other words, whether the surface excess at the solid-liquid interface is larger or smaller than that at the solid-vapor interface depends on whether u’” cos/3 increases or decreases with the solute concentration. Since there are standard methods6 of estimating the surface tension and the activity of a binary solution, a measurement of 8 or (T[”CO&Jas a function of the solute concentration would enable one to estimate r $’ - r “2”from Equation 11. One way of measuring u lU case is by performing the capillary flow experiments, in which the advancing of the liquid solution is a function of time in a capillary made of the solid material of interest. u’” cosf3 is then calculated from the Washburn equation’: ,lv
cos(j
=
z!&T Rt
other means. In other words, Equation 11 provides a possible way of verifying experimentally the Gibbs or Young’s equation. The surface excesses I’;’ and r? can be obtained experimentally. First, it should be noted that I’sr and rs,U in Equation 11 are defined such that r ;’ = 0 and ry = 0.Since experimental measurements are often made based on unit mass of the solid material, we write r2as r2 = ?jZ
(13)
s
where A, is the specific surface area of the solid and 7r2 is the surface excess amount per unit mass of the solid. The relationship between ~~ and the actual adsorbed amount is derived as follows. Suppose that on unit mass of the solid the individual adsorbed amounts are IZ~and n2, respectively, for components 1 and 2. Then imagine a (Gibbs) dividing surface that divides the total adsorbed amount n, + n2 into two parts: part 1 consists of the solute surface excess r2 (which is pure solute), and part 2 is the difference (nl + n2) - 7r2.The concentrations of components 1 and 2 in part 2 are defined to be, respectively, c,/(c, + c2) and c2/(c, + c2), where cl and c2 are, respectively, the concentrations of components 1 and 2 in the equilibrium bulk phase. Then a mass balance for the solute gives n, = (nl + n2 - 7r2)~ c2 +?7 2 Cl + c2
(14)
7~~= n2 - n, 22 cl
(15)
or
of 7r2reduces to that of n, and
Thus, the measurement
(12)
where L is the length of the liquid column at time, t, R is the radius of the capillary, and 77is the viscosity of the liquid solution. Once r$ - I’;U has been estimated, one may proceed further with more assumptions. For example, if it is assumed that r$ is nearly equal to rk, which can be calculated from Equation 2, then rp can be estimated. Another possibility is that in some cases I’$ is much greater than r;v and thus the value of I’$ - ry can be taken as an estimate of I’$. The previous discussions show that the adsorption behavior of a solid material can be qualitatively assessed through contact angle measurements or capillary flow experiments. Since all the quantities in Equation 11 can (in principle at least) be measured, its validity can thus be verified experimentally. Because Equation 11 is derived from the Gibbs equation and the Young’s equation, once the validity of Equation 11 is established the validity of the Gibbs equation (or the Young’s equation) would follow if the validity of the Young’s equation (or the Gibbs equation) is assumed or established by some
122.
Equation 15 is convenient to use in solid-vapor adsorption where the individual adsorbed amounts are often measured. But for solid-liquid adsorption, batch experiments are often performed where the reduction of the solute concentration in the bulk phase before and after adsorption equilibrium is observed. In this case, we derive another equation for 7~~as follows. Suppose that in a batch experiment, unit mass of the solid is mixed with n, amount of solution of solute concentration c~~.After adsorption equilibrium the solute concentration of the solution reduces to c2. Then a mass balance for the solute gives n, = (c20n0 - nl -
n2k2
+
n2
(16)
or c2=
no(c20
-
~2)
(17) 1 - c2 Since 1 - c2 = cl for a binary solution, from Equations 15 and 17 one obtains n2 -
4
= =
n&20
2
1 -
c2
-
~2)
(18)
1 - c2
Separations
Technology,
1991, vol. 1
283
Wetting and adsorption
of polymeric
resins: C. Yao, S. Shan and C. Tien
Finally, we would like to note that when a porous adsorbent is in contact with a liquid, true solid-liquid adsorption does not always take place. It is possible that (some) pores of the adsorbent are not invaded (or fully wetted) by the liquid, and thus in these pores solid-vapor adsorption takes place. Such is the case when hydrophobic resins (e.g., Amberlite XAD-4) are in contact with dilute aaueous solutions of oreanits. To obtain true solid-liquid adsorption isotherms for these resins, the common practice is to prewet them.
284
Separations
Technology,
1991, vol. 1
References 1. 2 ’ 3.
z: 6.
7.
Rixey, W.G. and Ring, C.J. J. Colloid Interface Sci. 1989,131, 320 Rixey, W.G. Nonwet adsorbents for the selective recovery of polar organic solvents from dilute aqueous solutions. Ph.D. thesis, 1987. University of California, Berkeley, CA, USA Yao, C. and Tien, C. AZChE J. 1989,35, 1559 Yao, C. and Tien, C. Reactive Polymers 1990, l3, 121 Adamson, A.W. Physical Chemistry of Surfaces. New York: John Wiley & Sons, 1976 Reid, RC:, Prausnitz, J.M. and Poling, B.E. The Properties of Gases and Liquids. New York: McGraw-Hill, 1987 Fisher, L.R. and Lark, P.D. J. Colloid Interface Sci. 1979,69, 486