Nanoreactor Effect in Bifunctional Cation Exchangers Based on Cis-Metacyclophanoctol

1331 | P a g e F e b r u a r y 0 7 , 2 0 1 4 Nanoreactor Effect in Bifunctional Cation Exchangers Based on Cis-Metacyclophanoctol Heinrich Altshuler, Olga Altshuler 1 Institute of Coal-chemistry and Material Science, Siberian Branch of Russian Academy of Sciences, 650000, Kemerovo, Russian Federation altshulerh@gmail.com 2 Kemerovo State University, 650043, Kemerovo, Russian Federation colo@list.ru ABSTRACT


INTRODUCTION
A nanoreactor is a nanosized container used for accommodating chemical reactions [1]. Nanoreactor increases the rate of diffusion with respect to bulk reaction due to the short pathway that reagent molecules need to follow to meet each other [1]. Cis-metacyclophanoctol molecule consisting of great hydrophobic cavity and the upper hydrophilic rim including eight hydroxylic groups [2] is a typical nanoreactor. Especially it is true for reactions associated with the self-assembly mechanism of proton transfer within the molecule [3].

Fig 1: An elementary unit of network polymers based on cis-metacyclophanoctol derivatives
As was previously reported in [7], bifunctional polymers 1 and 2 contain strongly acidic SO3H groups which dissociate with the formation of free protons over a wide pH range (0-14), and weakly acidic phenol OH groups. Monofunctional polymers 3 and 4, include only weakly acidic phenol OH groups. The thermodynamics and kinetics of ion exchange in polymers 1 -4 based on cis-metacyclophanoctol were investigated in [12][13][14][15][16]. It was shown [14][15][16] that the limiting stage of ion exchange kinetics is diffusion of ions in the polymers.
The purpose of the present work is mathematical description of cation flux in bifunctional polymers containing strongly and weakly acidic groups, particularly in bifunctional sulfonated polymers 1 and 2 based on cis-metacyclophanoctol.

Synthesis
Polymer 1 and 2 were produced by sulfonatation of monofunctional polymers 3 and 4 on according to the procedure [8]. The total dynamic ion-exchange capacities (in equiv. per 1 kg of the polymer in the H form dried at 105°С of the polymers) were 6.0 and 5.65 for polymers 1 and 2 respectively. The contents of acidic SO3H groups in polymers 1 and 2 were 1.86 and 2.45 equiv. per 1 kg of the dry H form of polymer.

Kinetic studies
For kinetic studies the selection of spherical granules and the determination of their sizes were performed using the IMTs 10050, A microscope. Polymer granule size distribution corresponded to a normal (Gaussian) distribution. The particle radius calculated as an arithmetic average of the size of 1000 spherical granules was (1.02 ± 0.53) ·10 -4 m.
The kinetics of ion exchange was studied by the dynamic thin-layer method [17] at 298 K by sorption from an infinite volume of electrolyte solutions with concentrations of 0.01, 0.03, 0.05 and 0.1 mol/dm 3 .

Calculation details
Molecular structure of the repeating unit of polymers was optimized in terms of enthalpy of formation by the semiempirical PM6 method within the MOPAC 2009 program, ion exchange kinetics and diffusion coefficients were calculated by iteration method within the MathCad 7 program. All calculations are fulfilled on Intel (R) Core(TM)2 Duo T7300 processor. F e b r u a r y 0 7 , 2 0 1 4

Ion exchange processes
The following ion exchange processes take place in bifunctional polymers 1 and 2: with participation of sulfonic acid groups with participation both sulfonic acid and phenol OH groups Here L -fragment of elementary unit of polymer based on cis-metacyclophanoctol.
In bifunctional polymers 1 and 2 it is possible to obtain phenolate LO -Cat + as a sum of processes (I) and (II). In monofunctional polymers 3 and 4 ion exchange process (III) take place only with phenol OH groups.
To choose the optimal technique of obtaining of phenolate of Cat + O --L it is necessary to compare the rates and mechanisms of processes (I) -(III).

Fundamental diffusion equation
The fundamental diffusion equation (1) in the case of constant diffusion coefficient and spherical symmetry is applied [18] if diffusion of ions in polymers is rate limiting stage of ion exchange Where Ddiffusion coefficient of the species; Сcurrent concentration of the species in a polymer; rradius-vector; ttime. Let us consider the solution of equation (1) for processes (I) -(III).

Solution of the diffusion equation for сation exchange process (I) in polymers 1 and 2 with participation of sulfonic acid groups
Early we investigated [15]  for the transformation degree (F) of ion exchanger [17] describes experimental data for exchange of protons by metal cations from SO3H groups of polymers [15]. Here, Mt -the amount of cations sorbed at time t; M  -equilibrium ion exchange capacity; Dw -effective diffusion coefficient in polymer, r0-average radius of spherical particle of polymer. The values of effective diffusion coefficient of cations in sulfonated polymer 2 based on cis-tetraphenylmetacyclophanoctol, calculated with probability 0.9 by equation (2), are in the (1.9 ÷ 2.1)10 -11 m 2 /s interval.

Solution of the diffusion equation for сation exchange process (II) in polymers 1 and 2 with participation both sulfonic acid and phenol OH groups
Before the beginning of process (II) bifunctional polymers 1 and 2 already contain Cat + whose concentration is equal to that of  3 SO groups. In process (II) the ion exchange of protons of phenol OH groups by Cat + takes place. The rate of process (II) with participation of polymers 1 and 2 is controlled by H + and Cat + interdiffusion in a spherical particle of a polymer.

Effective diffusion coefficient
According to diffusion mechanism of process (II) for constant diffusion coefficient DH of free protons, the flux equation is obtained [19]. Here, , Сat J -diffusion flux of cations, Ка -dissociation constant of phenol OH groups in a polymer, Cr -general concentration of fixed ionogens (ionized and not ionized hydroxyl groups) in a polymer.
Since swelling and hydration values of studied polymer 2 upon conversion (II) remain constant (30 mol H2O per 1 equiv. of total capacity of polymer), it can be to assumed that the effective diffusion coefficient in polymer Dw in equation (3) is F e b r u a r y 0 7 , 2 0 1 4 constant. Let us calculate its value. We take DH = 10 -9 m 2 /c [19,20]; Сr= 110 3 mol/m 3 . The value of Ka 10 -6 mol/m 3 is obtained by the data [7] of potentiometric titration of sulfonated polymers 1 and 2. Thus Dw which was calculated using equation (4) is equal to 10 -18 m 2 /s.

Spherical layer model for particle of polymer 1 or 2
We assume that the spherical particle of polymer 1 or 2 should consist of a set of spherical layers.   Cat SO 3 groups are located on the outer surface of each spherical layer while phenol OH groups nearest to them are on its inner surface ( Figure 2). The diffusion flux of Cat + through a spherical layer passes the distance between   Cat SO 3 and phenol ОН groups ( Figure 2). For non-steady state the solution of diffusion equation (1) can be obtained by Laplace transforms or a method of separation of variables [21] in case diffusion coefficient is constant. If the surface r = a is maintained at C1, and and r = b at C2, and the region a ≤ r ≤ b is initially at C0, the solution [21] of equation (1) is the expression The dependences of the transformation degree from   2 are shown in Figure 3 for different values of b/a. The top curve corresponds to solid sphere (a = 0), bottom -to plane sheet (b/a=1, r >> (b -a)). As can be seen from the Figure 3, the bottom curve describes the behavior of our system, it covers the whole range of experimental data of cation sorption from alkaline solutions with the participation of the hydroxyl groups of sulfonated polymer 2. Consider the data of ion exchange kinetics at polymer 2 based on cis-tetraphenylmetacyclophanoctol according to the theory of diffusion in a plane sheet.

Diffusion in a plane sheet for polymer particle
If r >> (ba), the spherical layer of polymer 2 can be regarded as a plane sheet or membrane, in which   Cat SO 3 groups are located on the outer surface of a plane sheet while phenol OH groups nearest to them are on its inner surface. Consider the case of diffusion through a plane sheet or membrane of thickness l with constant diffusion coefficient Dw, whose surfaces, x = 0, x = l, are maintained at constant concentrations C1, C2 respectively, a plane sheet is set initially at a uniform concentration C0.
It was shown [21] for non-steady state that the concentration of the species in a plane sheet is given by

Process (III). Cation -exchange on phenol hydroxyl groups of polymer 4
As was shown [19] the rates of ion exchange processes with participation of weakly acid ion exchangers are controlled either by interdiffusion of H + ions and sorbed Cat + cations or by diffusion of ОН anions in polymer. In this case the rate of the process (III) is controlled by diffusion of ОН anions in a polymer 4. The known [19] equation (11)

RESULTS AND DISCUSSION
According to equation (3), at constant diffusion coefficient, the diffusion flux depends only on concentration gradient. In monofunctional cation exchangers the value of the concentration gradient is determined by the change in the concentration of a diffusing component at a macroscopic distance from the outer surface of the ion exchange particle to its center. In bifunctional cation exchangers (polymer 1 and polymer 2) the cation diffusion flux passes the distance between   Cat SO 3 and phenol ОН groups. It is considerably less than the dimension of the ion exchange particle. In the repeating unit of polymer 2 the calculated distance is several nanometers (Figure 4). Based on the proposed model the length of diffusion path, i.e. (ba) in equation (8), or l in equation (10) equal to 30 nm. Large concentration gradient will increase the rate of the process (II).
Half-transformation periods of time (t at F = 0.5) calculated from the experimental data [14][15][16] are given in the Table 1.
As we seen from the table the process (I) of ion exchange H + -Cat + with participation of sulfonic acid groups of polymer 2 has the highest rate, the process (III) of sorption of cations Cat + from alkaline solutions with participation phenol OH groups of polymer 4 has the lowest rate.

Polymers
Process Ionogenic groups t, s at F = 0.5 Bifunctional polymer 2 I strongly acidic SO3H groups 16 Bifunctional polymer 2 II strongly acidic SO3H groups, weakly acidic phenol OH groups 50 Monofunctional polymer 4 III weakly acidic phenol OH groups 9500 Comparing the rates of ion exchange processes (II) and (III) with participation of weakly dissociating ionogenic groups at bifunctional and monofunctional cation exchangers, we find out the nanoreactor effect that consists in hundredfold increase in ion exchange rate on bifunctional cation exchangers. The cup of bifunctional cistetraphenylmetacyclophanoctol, which contains as strongly acidic SO3H groups and weakly acidic phenol OH groups ( Figure 4) immobilized in the network polymer phase, acts as nanoreactor.

CONCLUSION
The solutions of the fundamental differential equation of cation diffusion were used for investigation of ion exchange kinetics in sulfonated polymers based on cis-metacyclophanoctol. The mathematical model explaining the nanoreactor effect in bifunctional cation exchangers was proposed. It predicts considerable improvement of the kinetic characteristics S C O H F e b r u a r y 0 7 , 2 0 1 4 of cation exchangers containing weakly dissociating ionogenic groups when strong acidic functional groups are introduced into these cation exchangers. This effect holds good for both bifunctional polymers based on derivatives of cismetacyclophanoctol and other bifunctional cation exchangers (for example Amberlite IRA-100 type) for producing ionexchange membranes and selective sorbents.