Langmuir 2007, 23, 10081-10087
10081
Adsorption Kinetics of Carcinogens to DNA Liquid Crystalline Gel Beads Kazuya Furusawa,† Masako Wakamatsu,† Toshiaki Dobashi,† and Takao Yamamoto*,‡ Department of Chemistry and Chemical Biology, and Department of Physics, Faculty of Engineering, Gunma UniVersity, Kiryu, Gunma 376-8515, Japan ReceiVed May 14, 2007. In Final Form: July 4, 2007 Adsorption behaviors of acridine orange (AO) and biphenyl (BP) to DNA liquid crystalline gel (LCG) beads in aqueous dispersing solution have been studied theoretically and experimentally. A theoretical consideration based on nonequilibrium thermodynamics predicted that the time course of the adsorption process is expressed with a scaled equation, and a scaled number of adsorbed carcinogen molecules n˜ is expressed with the square root of a scaled immersion time ˜t, n˜ ∝ x˜t at early stage, whereas it is expressed with a power law function 1 - n˜ ∝ (t˜e - ˜t)3/2 for n˜ 0 > 1 and an exponential equation n˜ 0 - n˜ ∝ e-t/Rτ0 for n˜ 0 > 1 at later stages of adsorption. Here, n˜ 0 is the ratio of the initial number of carcinogen molecules in the dispersing solution to the number of the sites of adsorption of carcinogen molecules in the beads, ˜te is the scaled equilibrium time of adsorption, τ0 is a time constant for adsorption, and R is a constant. Observed adsorption processes for AO were well expressed by the predicted ones, and the fitting parameters n˜ 0 and τ0 increased with increasing cobalt chloride concentration CCo used for preparation of the beads, and both saturated above CCo g 400 mM for the adsorption of AO, whereas the adsorption processes for BP were expressed with the square root function. These results indicate that (1) the adsorption process at early stage is explained by diffusion-limited binding of the carcinogen molecules to DNA beads, and the time range of the early stage depends on the solubility (the solubility of AO in water is high whereas that of BP is low); and (2) the process at later stages depends on the balance of the numbers of adsorption sites and carcinogen molecules.
Introduction Recently, global air and water pollution by toxic chemical agents has grown into a serious problem. Particularly, halogenated compounds having aromatic planner groups such as polychlorinated biphenyl, dioxin, and benzopyrene result in mutation and endocrine disruption through intercalation into major grooves and interstices between base pairs of DNA double helices.1,2 This fact suggests that materials consisting of DNA or DNA composites can be utilized as the most efficient adsorbents for such toxic agents. For this application, the materials must usually be at a water-insoluble state. Several technological developments to prepare water-insoluble DNA compounds have been performed to create environmental cleanup materials.3-6 Nishi et al. succeeded in the insolubilization of salmon milt DNA by crosslinking it with ultraviolet irradiation4-5 and by forming molecular complexes with other biomacromolecules.3 Umeno et al. reported the synthesis and characterization of polyacrylamide gels containing DNA and their application as carcinogen adsorbents.6 Previously, we developed a DNA liquid crystalline gel (LCG) prepared from DNA-concentrated solutions by using dialysis into multivalent metal cation solutions.7 This new material is expected to be utilized as an intelligent probe and an adsorbent * Corresponding author. Fax: +81 277 30 1927. E-mail: yamamoto@ phys.sci.gunma-u.ac.jp. † Department of Chemistry and Chemical Biology. ‡ Department of Physics. (1) Lerman, L. S. J. Mol. Biol. 1961, 3, 18. (2) Dandliker, P. J.; Holmin, R. E.; Barton, J. K. Science 1993, 262, 1025. (3) Yamada, M.; Kato, K.; Nomizu, M.; Ohkawa, K.; Yamamoto, H.; Nishi, N. EnViron. Sci. Technol. 2002, 36, 949. (4) Yamada, M.; Kato, K.; Shindo, K.; Nomizu, M.; Haruki, M.; Sakairi, N.; Ohkawa, K.; Yamamoto, H.; Nishi, N. Biomaterials 2001, 22, 3121. (5) Yamada, M.; Kato, K.; Nomizu, M.; Ohkawa, K.; Yamamoto, H.; Nishi, N. Chem.sEur. J. 2002, 8, 1407. (6) Umeno, D.; Kano, T.; Maeda, M. Anal. Chim. Acta 1998, 365, 101. (7) Dobashi, T.; Furusawa, K.; Kita, E.; Minamisawa, Y.; Yamamoto, T. Langmuir 2007, 23, 1303.
of toxic agents with the advantage of having anisotropic optical properties and a high capacity to hold solvents. The kinetics of adsorption of toxic agents by DNA molecules has been studied,8,9 and the interaction was classified into external binding, groove binding, and intercalation. Especially, ethidiumDNA intercalation has been intensively investigated,10 and multistep kinetics have been proposed. Although the mechanism of adsorption of toxic agents into DNA composites could be explained by the combination of the above essential interactions, from the aspect of bioconjugate materials science and technology, it is more important to describe the adsorption behavior phenomenologically, because meso- and macroscale structures of the composites have a considerable effect on the adsorption behavior. In a previous preliminary study on the adsorption kinetics of acridine orange (AO) to DNA LCG beads,11 it was found that the adsorption time course of grams of AO adsorbed to one gram of DNA, Γ(t), was expressed by Γ(t) ) Γe(1 exp(-(t/τ)β), with the exponent β ∼ 0.7. This result suggests that the entire adsorption process is not explained with a simple diffusion model, but a more rigorous theoretical model is needed. In this study, to describe the experimental data and to analyze the adsorption behavior, we have developed a theory for the adsorption kinetics of carcinogen to DNA LCG beads by using nonequilibrium thermodynamics with simple assumptions. To compare the theoretical and experimental results, we found that the adsorption process at an early stage is explained by diffusionlimited binding of the carcinogen molecules to DNA beads, and that the time range of the early stage depends on the solubility, (8) Turro, N. J.; Barton, J. K.; Tomalia, D. A. Acc. Chem. Res. 1991, 24, 332. (9) Desfrancois, C.; Carles, S.; Schermann, J. P. Chem. ReV. 2000, 100, 3943. (10) For example, (a) Macgregor, R. B., Jr.; Clegg, R. M.; Jovin, T. M. Biochemistry 1987, 26, 4008. (b) Meyer-Almes, F. J.; Porschke, D. Biochemistry 1993, 32, 4246. (c) Wang, G.; Zhang, J.; Murray, R. W. Anal. Chem. 2002, 74, 4320. (11) Maki, Y.; Furusawa, K.; Wakamatsu, M.; Yamamoto, T.; Dobashi, T. Trans. Mater. Res. Soc. Jpn., in press.
10.1021/la701379q CCC: $37.00 © 2007 American Chemical Society Published on Web 08/21/2007
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while the process at later stages depends on the balance of the numbers of adsorption sites and carcinogen molecules. Experiment Sodium-type double-stranded DNA extracted and purified from salmon milt was provided from Japan Chemical Feed Co., Ltd. The nominal average base pair examined by electrophoresis was 10 kbp. Cobalt chloride and sodium tetraborate were purchased from Wako Pure Chemicals. Milli-Q water was used as solvent. A desired amount of DNA was dissolved in 20 mM sodium tetraborate aqueous solution at 1.0 wt %. In order to prepare DNA LCG beads, the DNA solution was poured drop by drop into cobalt chloride solutions with various concentrations in the range between 50 and 1000 mM at 25 °C. The interfacial layer formed by the initial reaction played the role of dialysis tubing, and dialysis from the spherical surface was performed to make small beads with almost the same diameter of 2-3 mm. Biphenyl (BP) and AO purchased from Wako Chemicals were used. For the measurements of adsorption of AO by DNA LCG beads, 0.3 g of the beads was immersed into 10 mL of aqueous solution of AO at 13µg/mL, which was gently stirred and thermally controlled at 25 °C. The optical density (A495) of the AO solution was measured at wavelength λ ) 495 nm as a function of immersion time t. The concentration of AO in the solution, CAO, was calculated from a calibration equation CAO ) 14.14 × A495 (µg/cm3) obtained by standard solutions with known concentrations. For the measurements of adsorption of BP by the DNA LCG beads, 1.2 g of the beads was immersed into 10 mL of aqueous solution saturated by BP (6.3 µg/cm3), which was gently stirred and thermally controlled at 25 °C. The optical density (A250) of the BP solution was measured at wavelength λ ) 250 nm as a function of immersion time t. The concentration of BP in the solution, CBP, was calculated from a calibration equation CBP ) 9.86 × A250 (µg/cm3).
Theoretical Analysis Let us consider a DNA gel bead with radius R in a solution of carcinogen molecules with volume V. To discuss the carcinogen molecule adsorption behavior, we adopt the following assumptions: (A) All carcinogen molecules flowing into the bead are used up to produce the adsorbed layer in which the DNA gel adsorbs carcinogen molecules up to the maximum density; all the adsorption sites are saturated with carcinogen molecules. (B) In the adsorbed layer, carcinogen molecules are not captured. These assumptions make us to pay attention to the boundary between the adsorbed layer and the non-adsorbed part of the bead, in which no carcinogen molecules are adsorbed. Then, the adsorption dynamics can be illustrated in terms of the “boundary-moving dynamics”. The moving boundary picture for illustrating diffusion and “adsorption” process was proposed to analyze the Curdlan LCG formation.12 It is valid when the carcinogen molecules flowing into the gel are adsorbed instantly or the carcinogen molecules hardly penetrate the nonadsorbed layer, whereas they penetrate the adsorbed layer relatively easily. Since the adsorbed behavior is spherically symmetric, the position of the boundary is expressed by the distance r from the bead center. In the spherical cell region (R g x g r, where x is the distance from the center), all the adsorption sites are occupied by carcinogen molecules (the adsorbed layer), and, in the sphere region (r g x g 0), all the adsorption sites are empty. The illustration of the model system and the notations are given in Figure 1. Here, n0, nf, Ff, and n(t) denote the number of carcinogen molecules in the dispersing solution at the initial state, the maximum number of carcinogen molecules that the DNA LCG bead is capable to adsorb, the maximum number density of carcinogen molecules adsorbed to the bead, and the number of (12) Nobe, M.; Dobashi, T.; Yamamoto, T. Langmuir 2005, 21, 8155.
Figure 1. Schematic illustration of the adsorption system. n0, nf, Ff, and n(t) denote the number of carcinogen molecules in the solution at the initial state, the maximum number of carcinogen molecules that the DNA LCG bead is capable to adsorb, the maximum number density of carcinogen molecules adsorbed to the DNA LCG bead, and the number of carcinogen molecules adsorbed to the bead at immersion time t, respectively.
carcinogen molecules adsorbed to the bead at immersion time t, respectively. The time development of the boundary r ) r(t) gives the time course of n(t). Since the flux of carcinogen in the adsorbed layer is spherically symmetric, the flux density vector of carcinogen flowing into the inner core is given by
B J ) -J(x)e br J(x) ) kF(x)
∂µ(x) ∂x
(1)
where b er is the unit vector along the radial direction of the gel bead, k is the mobility of carcinogen molecules, and F(x) and µ(x) are the number density and the chemical potential of carcinogen molecules at point x, respectively. In the adsorbed layer (R g x g r), the assumptions give the quasi-steady-state flow:
divJ B)-
2 1 ∂x J(x) )0 x2 ∂x
(2)
The solution of eq 2 is given by
J(x) )
C x2
(3)
where C is the integral constant. From eqs 1 and 3, we have
kF(x)
∂µ(x) C ) 2 ∂x x
(4)
Integrating both sides of the above equation from x ) r to x ) R, we have
k{F(R)µ(R) - F(r)µ(r) - f(F(R)) + f(F(r))} ) C
R-r (5) Rr
The left-hand side of eq 5 is rewritten as
k{F(R)µ(R) - F(r)µ(r) - f(F(R)) + f(F(r))} ≡ k(g(R) - g(r)) (6) Here, f(F) is the free energy of carcinogen molecules per unit volume; µ ) ∂f/∂F. The osmotic pressure of carcinogen molecules is expressed as
g(F) ) Fµ - f(F)
(7)
Adsorption of Carcinogens to DNA LCG Beads
Langmuir, Vol. 23, No. 20, 2007 10083 1/3 dn˜ (1 - n˜ ) (n˜ 0 - n˜ ) ) dt˜ 1 - (1 - n˜ )1/3
From eqs 5, 6, and 7, the constant C is expressed as
kRr C) (g(R) - g(r)) R-r
(8)
The number of adsorbed carcinogen molecules per unit of time is given by
dn ) 4πR2J(R) dt
(9)
Here note that τ0 ) V/(4πkkBTR) and n˜ 0 ) n0/nf. The solution of eq 19 is obtained by using the initial condition n˜ ) 0 at ˜t ) 0 as
˜t )
|
4πkRr [g(R) - g(r)] R-r
g(R) = kBTFs(t)
4πR2J(R) =
4πkRr k TF (t) R-r B s
-1
x3 (n˜ 0 - 1)
1/3
˜t )
]
|
|
n˜ 0 - n˜ (20) n˜ 0
[
2 - (n˜ 0 - 1)1/3 x3 -1 tan (n˜ 0 - 1)1/3 x3 (n˜ 0 - 1)1/3 tan-1
]
2(n˜ 0-1 - ν˜ )1/3 - (1 - n˜ 0-1)1/3
x3 (1 - n˜ 0-1)1/3
Using the spherical shape condition (4/3)πR3Ff ) nf, we have
with an integral expression of Q as
(
|
(
˜t ) Q(n˜ )
)
n(t) nf
+ ln
)|
(n˜ 0-1 - ν˜ )1/3 + (1 - n˜ 0-1)1/3 1 1 ln + 2(n˜ 0 - 1)1/3 1 - ν˜ n˜ 0-1/3 + (1 - n˜ 0-1)1/3
(13)
r(t) ) R 1 -
]
2(1 - n˜ )1/3 - (n˜ 0 - 1)1/3
+
+ ln|1 - ν˜ | (21)
Equation 20 is also represented as
4 3 4 3 πR - πr Ff 3 3
[
)| 3
Note that we always choose a real number cubic root of z for the expression of z1/3. Introducing a new variable ν˜ ) n/n0 ) n˜ /n˜ 0, we have a universal expression for the adsorption kinetics of carcinogen molecules to the bead:
(12)
On the other hand, the number of adsorbed carcinogen molecules can be related to the boundary position r(t) as
n(t) )
tan
(11)
where Fs(t) is the number density of carcinogen molecules in dispersing solution at time t, kB is the Boltzmann constant and T is the absolute temperature. Therefore, eq 9 is rewritten as
[
2 - (n˜ 0 - 1)1/3 x3 -1 tan (n˜ 0 - 1)1/3 x3(n˜ 0 - 1)1/3
(10)
Since the carcinogen molecules are not adsorbed to the inner core of the bead (x e r), the osmotic pressure of the carcinogen molecules is 0 there. On the surface of the bead, the osmotic pressure of the carcinogen molecules is equal to that of the dispersing solution. From the ideal gas approximation, we have
(
n˜ 0 (1 - n˜ )1/3 + (n˜ 0 - 1)1/3 1 ln 2(n˜ 0 - 1)1/3 n˜ 0 - n˜ 1 + (n˜ 0 - 1)1/3
From eqs 3 and 8, the right-hand side of eq 9 is rewritten as
4πR2J(R) )
(19)
1/3
Q)
(14)
(22)
3(1 - u)u
∫(11 - n˜ )
1/3
n˜ 0 - 1 + u3
du
(23)
If we use a new variable
From the mass conservation law
VFs(t) + n(t) ) n0
w)1-u
(15)
(24)
we have
we have
3(1 - u)u
n0 - n(t) Fs(t) ) V
(16)
4πkkBTR(1 - n(t)/nf)1/3 n0 - n(t) V 1 - (1 - n(t)/n )1/3
(17) Q(n˜ ) =
f
From eqs 9 and 17, the time development equation for n is given by 1/3 dn 4πkkBTR (1 - n(t)/nf) (n0 - n(t)) ) dt V 1 - (1 - n(t)/n )1/3
)
3w(1 - w) n˜ 0 - 1 + (1 - w)
3
=
3w n˜ 0 - 1
(25)
at the initial stage of the adsorption process; n˜ ≈ 0 (u ≈ 1 or w ≈ 0). Substitution of eq 25 into eq 23 gives us
Thus, from eqs 12, 14, and 16, we obtain
4πR2J(R) =
n˜ 0 - 1 + u
3
(18)
∫01 - (1 - n˜ )
1/3
3w 1 1 dw = n˜ 2 n˜ 0 - 1 6 n˜ 0 - 1
(26)
Thus, at the initial stage of adsorption, n˜ is proportional to the square root of ˜t:
n˜ ∝ x˜t
(27)
f
Equation 18 is rewritten with a scaled number of adsorbed carcinogen molecules, n˜ ) n/nf, and a scaled immersion time, ˜t ) t/τ0 as
The adsorption kinetics at the later stage depends on the value of n˜ 0 as follows: (1) In the case of n˜ 0 > 1, the adsorption sites in the bead can be saturated with carcinogen molecules, and all the carcinogen
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molecules are not adsorbed. The value of n can reach nf at a finite completion time te of adsorption. Thus, the value of n˜ reaches 1, or (1 - n˜ )1/3 vanishes at t ) te. From this condition, eq 23 is rewritten as
Q(n˜ ) )
∫(11 - n˜ )
1/3
3(1 - u)u n˜ 0 - 1 + u3
du = ˜t e -
3 1 (1 - n˜ )2/3 (28) 2 n˜ 0 - 1
where the scaled completion time ˜te ) te/τ0 gives
˜t e )
3(1 - u)u
∫01 n˜
0
du
- 1 + u3
(29)
Substitution of eq 28 into eq 22 gives
˜t e - ˜t =
3 1 (1 - n˜ )2/3 2 n˜ 0 - 1
(30)
Thus, the later process of carcinogen adsorption at n˜ 0 > 1 is expressed by the 3/2 power behavior as
1 - n˜ ∝ (t˜e - ˜t )3/2
(31)
(2) In case of n˜ 0 < 1, the carcinogen molecules are completely adsorbed to the bead, and some of the adsorption sites in the bead are vacant. The value of n approaches n0; n˜ approaches n˜ 0 when t f ∞. Near u = (1 - n˜ 0)1/3 (or large t region), we have an approximation expression,
3(1 - u)u n˜ 0 - 1 + u
∝ 3
1 u - (1 - n˜ 0)1/3
(32)
Substitution of eq 32 into eq 23 gives us
Q(n˜ ) ∝
∫(11 - n˜ )
1/3
du ) u - (1 - n˜ 0)1/3 -ln
(1 - n˜ )1/3 - (1 - n˜ 0)1/3 1 - (1 - n˜ 0)1/3
(33)
Thus, we obtain
(1 - n˜ )1/3 - (1 - n˜ 0)1/3 1 - (1 - n˜ 0)1/3
= e-t/Rτ0
(34)
where R is a constant. Finally, we have
n˜ 0 - n˜ ∝ e-t/Rτ0
(35)
Therefore, the later process of carcinogen adsorption to the bead at n˜ 0 < 1 is expressed by the exponential function. The results obtained for a single bead also hold for systems composed of many beads with the same radius. For many bead systems, V, n0, nf, and n(t) are regarded as the volume of the carcinogen molecule solution per one bead, the number of carcinogen molecules per one bead in the dispersing solution at the initial state, the maximum carcinogen molecule number one bead adsorbs, and the number of carcinogen molecules adsorbed to one bead at immersion time t, respectively.
Results Figure 2a,b shows the adsorption behaviors of AO and BP, respectively, to DNA LCG beads, and panels a and b of Figure
Figure 2. Time course of concentration of carcinogenic agents in medium: (a) AO for the DNA LCG beads prepared at CCo ) 50 mM (circle), 75 (square), 100 (triangle up) 200 (triangle down), 600 (diamond), and 1000 (hexagon); and (b) BP for the DNA LCG beads prepared at CCo ) 100 mM (circles), and 1000 mM (squares), respectively. The solid curves are drawn to guide the eyes. The down-arrows indicate the terminal time of the early stage at which the time course is expressed by eq 27, and the up-arrows indicate the starting time of the later stage at which the time course is expressed by eq 31 or 35.
3 are the plots suggested by eq 21. According to the theoretical consideration, the observed adsorption behavior is expressed in terms of the scaled number of adsorbed carcinogen molecules to the beads ν˜ (t) ) [((CCM0VCMNA)/MCM - (CCM(t)VCMNA)/ MCM)]/[(C0CMVCMNA)/MCM] ) n(t)/n0 as a function of scaled immersion time ˜t, where C0CM is the initial concentration of carcinogen molecules in the whole system, VCM is the volume of the dispersing carcinogen solution, NA is Avogadro’s number, MCM is the molar weight of carcinogen molecules, and the subscript CM denotes carcinogen molecules (AO or BP). The solid lines for AO are the calculated values using eq 21 with fitting parameters of n˜ 0 and τ0 determined by a least-squares method. The cobalt chloride concentration (CCo) dependences of n˜ 0 and τ0 for the adsorption of AO are shown in Figures 4 and 5, respectively. At low CCo (600 mM), n˜ 0 is larger than 1, as shown in Figure 4. The value of τ0 increases with increasing CCo in the range less than 400 mM, and is constant above that, as shown in Figure 5. For the adsorption of BP, the observed adsorption behavior could not be expressed by eq 21, but is well expressed by eq 27. Figure 6 a,b shows the scaled plots of the adsorption process for AO at the early stage at typical cobalt concentrations of 100 mM (n˜ 0 < 1) and 1000 mM (n˜ 0 > 1) for preparation. The straight lines in the plots of Figure 6a are consistent with the theoretical eq 27. Figure 7 is the plot for AO adsorption suggested by theoretical eqs 31 and 35 at the later stage. The straight lines
Adsorption of Carcinogens to DNA LCG Beads
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Figure 5. Time constant τ0 in eq 21 for the adsorption of AO determined by a least-squares fit as a function of the cobalt chloride concentration used for gel preparation.
Figure 3. Time course of scaled number ν˜ (t) of adsorbed AO (a) and BP (b) to the DNA LCG beads prepared at various cobalt chloride concentrations. The symbols denote the same meaning as the caption of Figure 2. The solid lines are calculated ones using eq 21 with fitting parameters for panel a, and eq 27 was used for panel b.
Figure 6. Scaled plots according to eq 27 for the early stage for adsorption of AO: (a) CCo ) 100 mM; (b) CCo ) 1000 mM. Figure 4. Scaled number of AO molecules n˜ 0 determined by a least-squares method as a function of the cobalt chloride concentration used for gel preparation.
also support the theory. The data for the adsorption of BP were not taken over the whole range including the near-equilibrium state. It should be noted that the AO and BP adsorptions induce little or no volume change in gel beads.
Discussion The rate of decrease of AO concentration (CAO) in the dispersing solution decreases with increasing the concentration of cobalt chloride used for the gel preparation, as shown in Figure 2a. The entire processes of AO adsorptions are well expressed by the
theoretically obtained scaled plot (eq 21) with fitting parameters of n˜ 0 and τ0, as shown in Figure 3a. Since AO molecules are cationic carcinogens, they are adsorbed not only by intercalation into the DNA double helices but also by electrostatic interaction between the negative charges of DNA and the positive charges of AO. Then, the AO molecule adsorption process well satisfies assumptions A and B. When the beads were prepared at high CCo, the negative charges of DNA molecules should have been highly neutralized by cobalt cations before the adsorption experiment: In the other words, the adsorption sites for electrostatic interaction are occupied by cobalt cations during the process of preparation of the beads, resulting in larger n˜ 0 at high CCo. Note that n˜ 0 is the ratio of the initial number of carcinogen molecules in the dispersing solutions to the number of the sites of adsorption of carcinogen molecules in the beads.
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Figure 8. Time course of scaled number V˜ ) ν˜ (t˜) of adsorbed BP to the DNA LCG beads prepared at CCo ) 100 mM (circles) and 1000 mM (squares) cobalt chloride concentrations. The solid lines were calculated using eq 40 with fitting parameters.
and 3, the time for reaching equilibrium is much larger for BP adsorption than for AO adsorption. Paying attention to the solubility difference between AO and BP in water (the solubility of BP is about 103 times smaller than AO), we obtain a simple explanation for the large difference in equilibrium times. In terms of the maximum solvable BP density FMAX in the gel, the maximum of the osmotic pressure is given by πMAX ) g(FMAX) (see eq 7). When the osmotic pressure of BP in the dispersing medium is larger than πMAX, the following extension for the osmotic pressure balance eq 11 is required; Figure 7. Scaled plots according to eqs 31 (a; CCo ) 100 mM) and 35 (b; CCo ) 1000 mM) for the final stage of the adsorption of AO.
kBTFs(t) ) σ + πMAX
The sign of n˜ 0 - 1 varies from negative to positive at around CCo ∼ 400 mM, as shown in Figure 4. Thus, in the case of n˜ 0 < 1, it is suggested that the carcinogen molecules in the dispersing solution are adsorbed completely to the beads in equilibrium, whereas, in the case of n˜ 0 > 1, a portion of the adsorption sites of the beads are still vacant; the critical cobalt concentration for full occupancy in equilibrium is around 400 mM. Figure 5 shows that the time constant τ0 increases with increasing cobalt concentration at low CCo (400 mM). The increase of τ0 with CCo at low CCo and saturation after full occupancy at high CCo are attributed to the relation between the mobility k of AO in the DNA LCG and the DNALCG structure. Since in high CCo LCG, the DNA and the cobalt concentrations are high, thermal diffusion motion of AO molecules are frequently blocked. Then, the mobility k decreases and τ0 increases with increasing CCo. Figures 6 and 7 show asymptotic behaviors at early and later stages that are also consistent with the theoretical prediction. The root-square plots in Figure 6 indicate that the adsorption process is limited by diffusion of carcinogen molecules in the beads. The straight lines in Figure 7 for the later stage also support the theoretical consideration; the adsorption process is represented by a power-law function with the exponent 3/2 in the case of n˜ 0 > 1 or by an exponential function in the case of n˜ 0 < 1, although we cannot exclude other functions from the present limited time range of data for the later stage. In Figure 2a, the terminal time of the early stage and the starting time of the later stage estimated roughly are indicated by down-arrows and up-arrows, respectively. In the intermediate time region between the times indicated by the down-arrows and up-arrows, the crossover behavior from the early stage to the late stage appears. On the other hand, the adsorption process for BP was expressed by eq 27 for the initial stage. As clearly observed in Figures 2
where σ is the gel bead surface tension for the osmotic pressure of BP molecules. Then, we have
(36)
4πkR(1 - n(t)/nf) 4πkRr ) π (37) π R - r MAX 1 - (1 - n(t)/n )1/3 MAX 1/3
4πR2J(R) )
f
and the scaled time development equation
(1 - n˜ )1/3 dn˜ ) dt˜ 1 - (1 - n˜ )1/3
(38)
where ˜t ) t/τ1 with
τ1 )
1 4πkRnfπMAX
(39)
Note that n0 does not appear in the above equations. From eq 38, we have
3 ˜t ) [1 - (1 - n˜ 0V˜ )2/3] - n˜ 0V˜ 2
(40)
If the maximum osmotic pressure πMAX is small, the “equilibrium time” τ1 is large. Then, even for long time intervals, we regard this as ˜t ≈ 0, n˜ ) n˜ 0V˜ ≈ 0. Therefore, we can adopt the approximation
3 1 [1 - (1 - n˜ 0V˜ )2/3] - n˜ 0V˜ ≈ (n˜ 0V˜ )2 2 6
(41)
and we have the following square behavior consistent with the result shown in Figure 3b:
t ∝ V˜ 2 (t , τ1)
(42)
Adsorption of Carcinogens to DNA LCG Beads
To evaluate the time constant τ1, the BP adsorption behavior is analyzed on the basis of eq 40, and the two parameters n˜ 0 and τ1 are obtained by a least-square method. We obtain the parameter values τ1 ) 5.5 × 106 s and n˜ 0 ) 0.16 for CCo ) 100 mM, and τ1 ) 4.0 × 106 s and n˜ 0 ) 0.20 for CCo ) 1000 mM. Thus, expected large values of τ1 are obtained. Using these parameters, the V˜ -t˜ relation for the BP adsorption is shown in Figure 8. The theoretical curves given by eq 40 are also shown (the solid lines). Figure 8 indicates that the idea of the extended osmotic pressure balance (eq 36) is valid. The time range of the observation is too narrow to obtain precise values of the parameters. To obtain the precise values, the data for a large t region are required. In enough large t regions, the osmotic pressure of BP in the dispersing medium may be less than the maximum osmotic pressure πMAX since Fs decreases. In these time regions, the theory for the AO adsorption expressed by eq 21 becomes suitable for explaining the BP adsorption behavior. The consistency of the experiments and theory also suggests that the liquid crystallinity of DNA LCG does not affect the adsorption behavior seriously. The difference of the adsorption behavior between AO and BP is attributed to the solubility difference.
Langmuir, Vol. 23, No. 20, 2007 10087
Conclusion The entire processes of adsorption of AO to DNA LCG beads were well expressed by a theoretical scaled equation derived on the basis of nonequilibrium thermodynamics (the moving boundary picture). The dependence of cobalt chloride concentration used for the preparation of the beads on the characteristic parameter n˜ 0 of adsorption is attributed to the adsorption site number difference, and τ0 is attributed to the mobility difference. The adsorption behavior at the later stage depends on the ratio of the initial number of carcinogen molecules in the dispersing solution to the number of the sites of adsorption of carcinogen molecules in the beads n˜ 0. The adsorption behaviors of AO and BP are apparently different. However, the difference is simply due to the equilibrium time difference induced by the solubility difference in water. The two apparently different adsorption behaviors are explained by the same theory based on the moving boundary picture. Acknowledgment. This work was partly supported by a Grantin-Aid for Science Research from JSPS Research Fellowships for Young Scientists (# 058J6825) and by a Grant-in-Aid for Science Research (C) from JSPS (# 16540366 and #19540426). LA701379Q
