To the question of the influence of a silanol cover on the protolytic properties of aminopropyl silica gels 222 D O I: 1 0. 15 82 6/ ch im te ch .2 02 0. 7. 4. 15 Filisteev O. V., Sharov A. V. Chimica Techno Acta. 2020. Vol. 7, no. 4. P. 222–228. ISSN 2409–5613 To the question of the influence of a silanol cover on the protolytic properties of aminopropyl silica gels O. V. Filisteev*, A. V. Sharov Kurgan State University 63 Sovetskaya st., Kurgan, 640020, Russia *email: filisteev@kgsu.ru Abstract. The paper proposes a model that describes the acid-base properties of amino groups grafted onto the surface, taking into account their interaction with silanol groups. For this, aminopropyl silica was chosen as an object with well-studied methods of preparation, structure and properties. The isotherms of sorption of hydrogen ions on aminopropyl silica were obtained by potentiometric method. The experimental points were analyzed numerically, taking into account the presence of an electric double layer, the presence of surface processes competing with the sorption of hydrogen ions, and the peculiarities of the behavior of silanol groups when the degree of surface filling with hydrogen ions changes. The resulting model makes it possible to carry out a prelimi- nary calculation of the sorption of hydrogen ions on the surface of aminopropyl silica. Keywords: functionalized sorbents; aminopropyl silica; protolytic properties; curves of po- tentiometric titration of sorbents Received: 03.11.2020. Accepted: 09.12.2020. Published:30.12.2020. © Filisteev O. V., Sharov A. V., 2020 Introduction To  describe the  reactivity of  the  surface groups of  sorbents, many numerical algorithms for the  analysis of complexation on the surface are used. They are based on the numerical solution of equations that make it possible to calcu- late the experimentally determined charac- teristics of surface equilibria. The equations are usually solved with respect to the values of the equilibrium constants. In addition to them, the roots of the equation can be other parameters of the system (capacity of DES, the proportion of certain groups from the total concentration, etc.). In this case, it is possible to use models that take in- to account DES (the theory of complexation on the surface, including the Guy-Chapman and Stern models, the CD–MUSIC model [1–5], and those operating without taking into account DES (models of chemical reac- tions, distribution of groups by equilibrium constants [6–9]). Common materials, most often obtained by surface modification, are sorbents con- taining basic nitrogen [10, 11]. Nitrogen- containing groups often interact with acidic groups on the surface, which makes it diffi- cult to quantitatively analyze their acid-base and complexing properties. In such cases, the  equilibrium constants with the  par- ticipation of nitrogen-containing groups are conditional with respect to the content of  interfering groups. A  typical example is the acid-base and complexing properties on the surface of various types of aminosili- cas. The presence of acidic silanol groups 223 leads to  the  fact that the  experimentally determined constants are significantly lower than the  tabulated ones for struc- tures similar to those present on the sur- face. The processes of interaction of surface groups with each other lead to different in- terpretations of the initial data, depending on the model used: the presence of several types of nitrogen-containing groups, dif- ferent in the energy of sorption interaction with ions in solution, the presence of inter- actions of nitrogen-containing groups with each other, etc. [6, 8, 11–13]. At the same time, a model of the interaction of basic ni- trogen-containing groups with acidic ones on the surface has not yet been constructed. The available models require the involve- ment of a significant amount of preliminary obtained experimental data [14]. The pres- ence of such a model would allow a prelimi- nary calculation of the sorption properties of materials with the properties described above. In  this work, we propose a  variant of  describing the  interactions of  amino groups and silanol groups on the surface of aminopropyl silica gels during the ad- sorption of  hydrogen ions from a  solu- tion. The model takes into account the ef- fect of the diffusion double layer, as well as the direct chemical interaction of amino and silanol groups. Experimental Aminopropyl silicas were chosen as test objects as  materials with well-studied methods of  synthesis, surface structure, and acid-base properties [8]. For the syn- thesis of  aminopropyl silicas, industrial silica gels KSKG and KSMG were used. Silica gels were preliminarily crushed and divided into fractions by  sieving (used fraction 0.25–0.5 mm). The particles were separated from the dust by repeated wash- ing in distilled water. Before inoculation, the silica gels were heated at a temperature of  150 °С  to  constant weight. The  graft- ing of aminopropyl groups was carried out by impregnation of silica gels in solutions of  3-aminopropyltriethoxysilane (Acros Organics) in  anhydrous toluene [15]. To obtain samples with different surface concentration of amino groups, different temperatures and contact times were used. The  impregnation time was varied from 20  min to  24  hours, the  temperature  — from room temperature to 60 °C. The  moisture content of  the  samples was determined by  heating at  150  °C to  constant weight using an  automatic Sartorius analyzer. The  specific surface area was determined by  the  multipoint BET method from nitrogen sorption iso- therms at –196 °C on a SORBI MS analyzer. The  surface concentration of  aminopro- pyl groups was determined by the Kjeldahl method. The  curves of  potentiometric titra- tion of  the  samples were recorded using the  method of  one sample as  follows. A  weighed sample with a  known mois- ture content of  about 0.3  g, weighed on an  analytical balance, was mixed with 30 ml of a 0.1 M potassium chloride so- lution. The  cell with the  suspension was placed in  a  thermostat with a  tempera- ture of  25  °C.  Titration was carried out with 0.0500 M hydrochloric acid solution (fixanal). The indicator system was a glass electrode and a  silver chloride reference electrode. The measurement of pH up to 3 decimal places was carried out on an “Ex- pert 001” ionomer. The  time to  reach equilibrium after adding each portion of the titrant is not less than 15 minutes. Equilibrium at each point was considered 224 to  be achieved if the  pH did not change within 5 min by more than 0.002 units. Processing of experimental curves The  obtained experimental points were transformed into the  dependence of the surface charge on pH. The surface charge was calculated using Eq. (1). ( )H e k H F C SC + + ‑   σ = (1) Here σe is the surface charge calculated from the experimental data, C/m2; H C +  — total concentration of  hydrochloric acid in solution, mol/l; [H+] — concentration of hydrogen ions in solution, mol/l; S — specific surface area, m2/g; Ck — concentra- tion of silica suspension, g/l. The  concentration of  hydrogen ions in the solution was calculated from the pH values, taking into account the activity co- efficients of hydrogen ions in the solution. When analyzing the  experimental points, the following surface chemical pro- cesses were taken into account. –NH2s + H + s = –NH3 + s (2) ≡SiOHs = ≡SiO – s + H + s (3) The ‘s’ index indicates that the particles belong to the surface layer. From the charge balance condition, it follows that the  surface charge σ, calcu- lated from the concentration of particles determining the charge, can be expressed by Eq. (4): ( )s sNH SiO–3 – k F SC +   σ = ‑ ≡    (4) Equilibrium concentrations of ammo- nium groups and deprotonated silanols were calculated based on the material bal- ance conditions: [ ]NH s s sNH NH2 2 3–C + ‑  = ‑ +   (5) [ ]SiOHs s sSiOH SiO–C≡  = ≡ + ≡  (6) where NH s2 C‑ and SiOHsC≡ are the total con- centration of  surface amino groups and silanol groups, respectively. Taking into account Eqs. (5) and (6), expression (4) takes the form: NH s SiOHs k s s s H H 2 1 1 1 C CF SC K K ‑ ≡ + +       σ = ‑    + +     (7) In  Eq.  (7), K and Ks are the  equilib- rium constants of Eq. (2) and (3), respec- tively. The transition from the concentra- tion of hydrogen ions in the surface layer to the concentration in the bulk of the solu- tion was carried out using the well-known equation: sH H 0 , F RTe ψ ‑ + +   =    (8) where ψ0 is the potential in the zero plane relative to the solution volume. It was de- termined through the equation of the dif- fuse DES model: sinh0.1174 , 2 F I RT ψ σ = ‑ (9) where ψ is the potential of the beginning of the  diffuse layer, which is  taken to  be equal to the potential ψ0 [16]. Eqs. (8) and (9) were substituted into (7), yielding the simplified expression: e 2 1 0 ( ) n i iis n = σ ‑σ = ∑ (10) In  Eq.  (10), σei and σi are the  surface charges calculated by using Eq. (1) and (7), respectively, and n is  the  number of  ex- perimental points. Numerical minimiza- tion was performed using the built-in tools 225 of  Mathematica 10 software package. The  chosen parameter for minimization in all cases was the constant K. The acid- ity constant of  silanol groups, 7.67, was taken from [14]. The total concentration of  silanol groups, SiOHsC≡ , participating in the process is difficult to determine ex- perimentally. Therefore, this value was also an adjustable parameter during minimiza- tion. The evaluation of the results of mini- mization was also carried out according to the value of s0. Results and discussion When choosing K and SiOHsC≡ by mini- mizing Eq. (7), the following results were obtained. The  logK grows to  the  values in the range of 9.9–10.32 in comparison with conditional constants determined without taking into account the influence of silanol groups. In this case, the s0 distri- bution over the values of the surface con- centration is observed, shown in Fig. 1a. The shape of the points indicates an in- crease in  the  deviation of  the  calculated from the experimental points with an in- crease in  the  surface concentration (not a random nature of the distribution of s0 on the  NH s2 C‑ scale). Fig. 1b shows examples of approximation of experimental points of charge versus pH dependence. For low concentrations of grafted groups, the de- viation is not very significant. It is seen that the greatest deviation at high concentra- tions of amino groups is observed at low degrees of surface coverage with hydrogen ions. Thus, Eq. (7) is not suitable for fitting the points of titration curves. The non-random nature of the distribu- tion of points in Fig. 1a speaks of a regular- ity that we did not take into account when calculating. We assumed that an increase in the degree of saturation of the surface of  aminosilica with hydrogen ions leads to  a  change in  the  total surface concen- tration of silanol groups SiOHsC≡ , involved in process (2). In this case, the constancy of the constants of protonation of amino groups and acid dissociation of  silanol groups is postulated. To  reveal the  type of  dependence of the total concentration of silanol groups on the  degree of  titration of  the  surface from Eq.  (7) with Eqs. (8) and (9) sub- Fig. 1. Dependence of s0 values on the surface concentration of amino groups (a); examples of approximation of experimental points by Eq. (7) (b): 1 — sample with NH s2C‑ = 0.67 μmol/m 2, 2 — sample with NH s2C‑ = 3.33 μmol/m 2 226 stituted there, we expressed SiOHs .C≡ We used different values of logK in the vicinity of the propylamine protonation constant in solution: logK = 9, 10 or 11. Substituting the experimental values [H+] into the re- sulting equation, the desired dependence was obtained. Examples of  the  obtained dependences are shown in Fig. 2. For all samples in  the  range of  total hydrogen ion concentrations used by us, the dependences have a linear form. Based on this, SiOHsC≡ in Eq. (7) can be expressed as SiOHs ,bC a x≡ = + (11) where x is  a  parameter associated with the course of the titration process (titrant volume, total concentration of hydrogen ions), a and b are parameters selected for the  numerical minimization of  Eq.  (7). The  approximation results are shown in Fig. 3. The  curves in  Fig.  3 indicate in  fa- vor of the fact that the model used by us satisfactorily describes the  protonation of aminopropyl silicas with allowance for the  effect of  silanol groups on the  sur- face. The  mean value of  the  logarithm of the protonation constant is 10.55, which is  close to  the  thermodynamic constant of protonation of propylamine in an aque- ous solution (logK = 10.5 [17]). Compari- son of  the  a  constant with the  concen- tration of  amino groups on the  surface indicates that a is equal to the concentra- tion of grafted amino groups. Thus, the in- teraction of  amino groups with silanol groups in a 1:1 ratio is confirmed within the framework of this model. The average value of  the  b constant is  –0.0014. Most likely, its value corresponds to  the  rate of  decrease in  the  equilibrium concen- tration of amino groups with an increase in the degree of titration. From the  point of  view of  equilib- ria in  solutions, the  thesis of  a  decrease in the total concentration of one of the par- ticipants in  the  process does not stand up to criticism. However, on the surface of a solid, the groups are localized at spe- cific points on the surface. The transfor- mation of  an  amino group into an  am- monium one leads to  the  disappearance of  its interaction with silanol ones. Ac- cordingly, the  assumption of  a  decrease in the total number of silanol groups par- Fig. 2. Examples of obtained SiOHs HCl( )f VC≡ = dependences Fig. 3. Approximations of surface charge points calculated from experimental data by calculated lines: 1 — NH s2 C‑ = 0.65 μmol/m 2, 2 — NH s2C‑ = 0.90 μmol/m 2, 3 — NH s2C‑ = 1.51 μmol/m 2 227 ticipating in equilibrium with an increase in the number of protonated amino groups seems logical. A change in the concentra- tion of silanol groups during the process is equivalent to a different effect of silanol groups on amino groups that are unevenly distributed over the surface. The  model described in  the  work al- lows one to  carry out a  preliminary cal- culation of the isotherms of the sorption of hydrogen ions on aminosilica. For this, the  ionization constant of  propylamine in  an  aqueous solution and the  concen- tration of aminopropyl on the surface are used. The only empirical parameter is the b constant. 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