CATION DIFFUSION IN BIFUNCTIONAL POLYMERS
BASED ON CIS-TETRAPHENYLCALIX[4]RESORCINARENE
H. N. Altshuler, O. H. Altshuler
Kemerovo division of Institute of Solid State Chemistry and Mechanochemistry SB RAS,Kemerovo, Russia
Abstract.The kinetics of ion exchange in network bifunctionalized polymers containing sulfonate and phenol hydroxyl as ionogenshas been studied. It is shown that interaction of the investigated polymers with water solutions of electrolytes is controlled by diffusion of ions in a polymeric phase. For non-steady state the solution of the fundamental differential equation of cation diffusion in functionalized polymers by means of the model of a spherical layer is obtained for a variety of initial and boundary conditions provided the diffusion coefficient is constant.The nanoreactor effect consisting in great rate increase cation diffusion flux in bifunctionalized polymers containing sulfonate and phenol hydroxyl groups as ionogen was found.The proposed mathematical model explains the nanoreactor effect in bifunctional polymers.
INTRODUCTION
Recently, the chemistry of novel hybrid functional materials is aimed at creating the closed nanoreactors.
Calixarene having the hydrophobic cavity surrounded by hydrophilic groups is a typical nanoreactor[1].Earlier [2-5], we synthesized new network functionalized polymers by the catalytic resol polycondensation of calix[4]resorcinarene deriva-tives with formaldehyde.In works [6, 7] network polymers based on cis-calix[4]resorcinarene for the first time are used as matrixes to create solid spacenanoreactorsfor catalytic hydrogenation.Thethermodynamics of an ion exchange in calixarenecontaining polymers was investigated [8].
The purpose of this work was to determine the limiting stage of an ion exchange and to make the mathematical description of non-stationary transport of cation flux insolid space nanoreactors based on immobilized tetraphenylcalix[4]-resorcinarene, functionalized bysulfonate and phenol hydroxyl groups.Polymers1and2 containing the following formula of the repeating unit:
are selected as objects of research.
RESULTS AND DISCUSSION
Bifunctional polymers based on immobilized calix[4]resorcinarenes participate in the following processes of an ion exchange with single charged cations:
on sulfonate groups
on phenol hydroxyl groups
where L - a fragment of calix[4]resorcinarene immobilized in a polymer; Cat+ – Li+, Na+, Ag+, .
The kinetic dependences of the degree of transformation F on time t1/2for processes (I) - (III) are resulted in Fig. 1.
Fig. 1.Kinetic dependences of processes (I), (II), (III) of sorption of metal cations at polymers basedon cis- tetraphenylcalix[4]resorcinarene from aqueous solutions:1-NaCl, 2 – NaOH, 3 – LiCl, 4 – LiOH, 5 – AgNO3, 6 – (CH3)4NOH. (I) - H+ – Cat+ ion - exchange on sulfonate groups of polymer 2 on the data [9]; (II) - Cat+ sorption from alkaline solutions with participation of hydroxyl groups of polymer 1 on the data [10]; (III) - Cat+ sorption from alkaline solutions with participation of hydroxyl groups of sulfonatedpolymer 2.
Degree of transformation calculated as, whereМt - the amount of cations sorbed to the time t;M- equilibrium ion- exchange capacity.It is seen from Fig.1 that ion -exchange H+– Cat+ for sulfonate groups of polymer 2 has the highest rate (fig. 1, (I)), sorption process of cations Cat+from alkaline solutions with participation phenol hydroxylgroups of polymer 1 has a minimal rate (fig. 1, (II)).
Rectilinearity of dependences of the degree of transformation Ffrom t1/2at F 0.5(factors of linear correlation exceed 0.99) and passage of lines through the beginning of coordinates(Fig. 1) according to the criteria [11] testify that the interaction of polymers basedoncis-tetraphenylcalix[4]resorcinarene with aqueous solutions of electrolytes is controlled by diffusion of substance in polymer. Thus, a particle-diffusion ion-exchange kinetics takes place.
The particle-diffusionion-exchange kineticsat spherical symmetry in case of constant diffusion coefficient is described [11] by differential equation
(1)
Where D – diffusion coefficient of species;С –the current concentration of species in a polymer;r –radius -vector.
Process (I). Cation-exchange on sulfonate groups at polymer2
The expression [12]
(2)
for the degree of transformation of a monofunctional ionexchangerdescribes experimental datain all the researched range of concentrations for exchangeof protons from SO3H - groups at sulfonated network polymer 2 by metal cations from solution (Fig. 1, (I)). Here, Dw - effective diffusioncoefficient in polymer, r0- average radius of spherical particle of polymer. Values of an effective diffusion coefficient of cationsin a sulfonated polymer based on cis-tetraphenyl-calix[4]resorcinarene, calculated with probability 0,9 by equation (2), are in the interval(1.9 ÷ 2.1)10-11m2/s.
Process (II). Cation-exchange on phenol hydroxyl groups at polymer 1
The rate of the process (II) is controlled by diffusion of ОН–anions in a polymer.
The known [13] equation (3)
(3)
describes experimental data of ion-exchange rates in polymer1(Fig. 1, (II)) in all the researched range of concentrations.HereDOH - diffusion coefficient of ОН–anions in polymer, - concentration of ОН–anionson the surface of a spherical particle of a polymer,Cr- general concentration of fixed ionogens (ionized and not ionized hydroxyl groups) in a polymer.
Process (III). Cation-exchange on phenol hydroxyl groups at polymer 2
Here, initial sulfonatedpolymer2already contains Cat+cationswhose concentration is equal to that of -groups. In process (III) the ion- exchange of hydroxylgroup protons bya Cat+cationfrom an alkaline solutiontakes place. Concentration of co-ions (free ОН–anions) introduced from the diluted solution in to the ionexchanger containing a significant amount of ionized sulfonate groups is very small because of Donnan effect.The rates of process (III) at sulfonatedpolymer based on calix[4]resorcinarenes are controlled by H+and Cat+interdiffusion in a spherical particle of a polymer.
According to diffusion mechanism for process (III) at constant diffusion coefficient of free protons the flux equation [13]
. (4)
is obtained.
Here,, at (Ка- dissociation constant of fixed hydroxyl groups in a polymer).
Since swelling and hydration of researched polymer2upon conversion (III) remain constant (30 molH2Oon 1 g-equ.of full capacity of polymer), it is possible to assume, that the effective diffusion coefficient in polymerDwin equation (4) is constant. Let us calculate its magnitude.=10-9m2/s[13], mol/m3.Potentiometrictitration of sulfonated calixarenecontaining polymers [4] gives the magnitude Ka10-5mol/m3. Thus, the effective diffusion coefficientDw,calculated by the equation (5),is equal 10-17 m2 /s.
Model
As the rate of delivery of Cat+cations from solution to - groups is high, the flux of Cat+cation diffusion duringprocess (III) determined by the differential equation (4), will be actually directed from sulfonate-groupstohydroxyl groups of bifunctional polymer2(Fig. 2).
We assume that the spherical particle of polymer consist of a set of spherical layers. Sulfonate-groups are located on the external surface of each spherical layer and hydroxylgroups are on its internal surface (Fig. 2). The surface r = ais maintained at C1, and r = bat C2, and the region arbis initially at C0.For non-steadystate the solution of the diffusion equation (1) can be obtained by Laplace transformation method or method of separation of variables [14] provided the diffusion coefficient is constant. It results in function C(r,t), after its integration[14] the total amount of Cat+, which accumulates in the spherical layer after time t, is
(6)
When С0 = 0, С1 = 0, С2 =
(7)
(8)
Degree of transformation in time t is
(9)
In special case, if а= 0; b= r0, we obtain equation (2).
Graphs of F against are shown in Fig. 3 for different values of b/a.
The top curve corresponds to solid sphere (a= 0), bottom - to plane sheet (r> (b-a)).In the 0 F 0.5 range the experimental values correspond to the chosen model at small valuesb-a. According to equation(9), the rates of process (III) do not depend on the concentration of a solution, and concentration of polymer (at 0), probably, neither on the form and size of a spherical particle of a polymer. Actually, experimental valuesF(t1/2) for exchanges Н+ – Li+, Н+ – Na+ at various values of solution concentration are described by the same functional dependence (Fig. 1, (III)).
Fig. 3.DependenceFon. Curves - calculation; dots - experiment:1- cation sorptionfrom 0.1 mol/dm3 NaOH solutions; 2- cation sorptionfrom 0.03mol/dm3 NaOH solutions; 3-cation sorptionfrom 0.05 mol/dm3 LiOH solutions by sulfonated polymer 2 (process(III)).
Nanoreactor effect
In the case of constant diffusion coefficient,according to equation (4), the diffusion flux depends only from concentration gradient.At monofunctional polymer1the magnitudeof concentration gradient is determined by changingthe concentration of diffusion species at a macroscopical distance from an external surface of an ionexchanger particle to its center.At bifunctional polymer2 the cation diffusion flux overcomes the distance between and ОН – groups (Fig. 2) which is the value of molecular size and essentially less than the dimension of an ionexhanger particle. In the repeating unit of polymer 2 the distance is 1-2 nanometers. This results in essential increase in the rate of process (III).At the same time the rate of process (III) should be less than that of process (II) which provides for the delivery of cationsfrom a solution to sulfonate-groups of polymer.Half-transformation times (tatF= 0.5), calculated from the experimental data (Fig. 1), are equal: for process (I)16s, for process (II)9500 s, for process (III)50 s. Comparing the rates of ion-exchange with participation of weakly dissociated ionogen at monoand bifunctional polymer, we find out the nanoreactor effect, consisting in hundredfoldincrease of ion- exchange rate.
ACKNOWLEDGEMENTS
The authors would like to thank the Russian Foundation for Basic Research for financial supporting of this work (project № 07-03-96030).
REFERENCES
1.BuchachenkoA.: Chemistry on the border of two centuries — achievements and prospects. Russian Chemical Reviews 1999 68 (2) 85-102.
2.Altshuler H., Ostapova E., Fedyaeva O., Sapozhnikova L., Altshuler O.:Novel network polymers based on calixresorcinarene. Macromol. Symp. 2002 181 1-5.
3.Altshuler H., Sapozhnikova L.,Ostapova E., Fedyaeva O., Altshuler O.: Cationites based on calix[4]resorcinarene derivates. Solvent Extraction and Ion Exchange 2002 20 (2) 263-271.
4.Al’tshuler O., Sapozhnikova L. Al’tshuler H.:New sulfonate-containing network polymers based on immobilized cis -metacyclophane-3,5,10,12,17,19,24,26-octolsPolymer Science Series A2007 45 (7) 1198-1206.
5.Altshuler H., Abramova L., Altshuler O.: The Production Way of Polymeric Cationits(Variants), Russian Federation patent, Pat №2291171, January 2007.
6.Al’tshuler H., Sapozhnikova L.:Synthesis of ultradisperse transitive metals in immobilized microreactors Journal of structural chemistry2004 45 Supplement 178-182.
7.Al’tshuler H., Sapozhnikova L.:Preparation of ultradispersed transition metals in immobilized microreactors Russian Journal of Applied Chemistry 2004 77 (11)1896-1898.
8.Al’tshuler H., Sapozhnikova L., Ostapova E., Al’tshuler O.:The thermodynamic characteristics of ion exchange in a sulfonated polymer based on cis -tetraphenylcalix[4]resorcinarene. Russian Journal of Physical Chemistry A. 2007 81 (7) 1011-1015.
9.Al’tshuler H., Malyshenko N., Shkurenko G.: Kinetics of cation exchange on sulfonic polymer based on immobilized cis -tetraphenylcalix[4]resorcinolarene. Russian Journal of Applied Chemistry 2007 80 (10) 1737-1740.
10.Al’tshuler H., Fedyaeva O.: Kinetics of cation exchange on calixarenecontaining polymer. Russian Journal of Physical Chemistry 2001 75 (11) 2088-2089.
11.Helfferich F.: Ionenaustauscher. Weinheim, Verlag Chemie, 1959.
12.Boyd G., Adamson A., Myers L., jr.: The echange adsorption of ions from aqueous solutions by organic zeolites. II. Kinetics. J. Am. Chem. Soc. 1947 69 2836.
13.Helfferich F.: Ion-exchange kinetics. V. Ion exchange accomponied by reactions. J. Phys. Chem. 1965 69 (4) 1178-1187.
14.Crank J.: The matematics of diffusion. Oxford, Calendon Press, 1975.
9-1