Influence of diosgenin structure on the polymerization kinetics of acrylamide: An experimental and theoretical approach

Journal of Molecular Structure 985 (2011) 34–47

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Influence of diosgenin structure on the polymerization kinetics of acrylamide: An experimental and theoretical approach Oscar F. Odio a, Ariel Martínez a, Ricardo Martínez a,⇑, Rachel Crespo-Otero b, Luis A. Montero-Cabrera b a b

Laboratorio de Polímeros, Instituto de Ciencia y Tecnología de Materiales, Universidad de La Habana, Havana 10400, Cuba Laboratorio de Química Computacional y Teórica. Facultad de Química. Universidad de La Habana, Havana 10400, Cuba

a r t i c l e

i n f o

Article history: Received 21 July 2010 Received in revised form 1 October 2010 Accepted 4 October 2010 Available online 8 October 2010 Keywords: DFT Diosgenin Kinetics Polyacrylamide Radical polymerization Transfer reaction

a b s t r a c t The acrylamide polymerization in presence of diosgenin has been investigated by experimental and theoretical methods. NMR spectroscopy shows the absence of copolymerization. Viscosimetric and dilatometric experiments support the occurrence of transfer reactions that retard the polymerization. The mechanism was studied at the MPWB1K/6-31G(d,p)//B3LYP/6-31G(d,p) level of theory. Transfer, homopropagation, copolymerization and reinitiation reactions were considered either in gas or solution phase. According to results, the retardation seems to be originated by the formation of an allylic radical in the ring B of diosgenin that reinitiates acrylamide polymerization at slow rate. Ó 2010 Elsevier B.V. All rights reserved.

1. Introduction Nowadays, the exogenous use of plant growth regulators (PGR) has become important in agriculture. Modifications of PGRs to achieve a controlled release system have been the subject of many investigations [1–4]. Phytoactive polymers offer a successful solution, which consist in a macromolecular chain with the PGR bonded by an hydrolyzed group [5–7]. These formulations give some advantages over direct use of PGRs. They have a wider range of effective concentration; allow more suitable application and handling due to its high water solubility and show smaller environmental toxicity. Among the families of PGRs, we focused on synthetic analogues of brassinosteroids. These compounds show a high phytoactivity and anti stress properties. Diosgenin (DGN) [(3b,25R)-spirost-5en-3-ol] is a steroidal sapogenin used as starting material for the synthesis of brassinosteroid analogues with an equatorial hydroxyl group in C3 and a double bond between C5 and C6 in ring B (Fig. 1). The strategy of synthesis consists in the copolymerization of a vinylic ester (e.g. maleate or fumarate) of the PGR with a high water soluble monomer as acrylamide (AM). The double bond in ⇑ Corresponding author. Address: Instituto de Ciencia y Tecnología de Materiales, Zapata y G, Vedado, Havana 10400, Cuba. Tel.: +53 7 8707666; fax: +53 7 8794651. E-mail addresses: [email protected] (O.F. Odio), [email protected] (R. Martínez), [email protected] (R. Crespo-Otero). 0022-2860/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.molstruc.2010.10.006

DGN could produce side reactions like addition of acrylamide radicals to C5 and/or hydrogen atom abstractions from a carbon adjacent to the p system or near to the oxygen atoms in the spiroketal moiety. We investigated these reactions employing theoretical calculations. Theoretical methods are useful tools to understand and systematize many complex polymeric processes comprising radical reactions [8]. Thermodynamical and kinetic properties have been reported for initiation [9,10], homo [10–12] and copolymerizations [13], transfer reactions [14–17], degradation mechanisms [18] and tacticity predictions [10]. Due to the number of atoms involved in these reaction systems, the vast majority of the papers employed Density Functional Theory (DFT) methodologies, since they provide acceptable results at moderate computational times. Our main aim was to investigate the suitability of diosgenin as a model compound for the successful synthesis of amphiphilic copolymers based in polyacrilamide (PAM). We focus our attention on the reactions that take place during radical polymerization of AM with DGN, in particular around its double bond and the spiroketal chain. Experimental kinetic studies by dilatometry were complemented with viscosimetric molecular mass determinations and NMR measurements. Transfer reactions were modelled at the MPWB1K/6-31G(d,p)//B3LYP/6-31G(d,p) level of theory, as well as the homopropagation step and reinitiating events to test the kinetic features of the whole process. A polarizable continuum model was used in order to take into account the effect of solvent.

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35

2.1.2. Viscosimetry Polyacrylamide samples were prepared in the same way as for the copolymerization study. In one experiment 0.05 mol of AM, 2  103 mol of DGN and 0.2  103 mol of AIBN were mixed in 50 mL of THF. Temperature was fixed at 50 °C and the reaction was refluxed for 2 h. Subsequently, the solid obtained was filtered, washed three times with 5 mL of fresh THF and dried under vacuum. In the other experiment, all conditions were held constant but DGN was removed. Viscosity measurements were conducted in an Ubbelohde viscosimeter at 30 °C. Water solutions of different concentrations (ranging between 12 and 20 kg/m3) of both polymer samples (PAM and PAM–DGN) were prepared in situ. The time of flow for each solution was recorded starting from the more concentrated.

2. Experimental part

2.1.3. Dilatometry In a typical experiment, the acrylamide monomer, the steroid and the initiator were dissolved in 10 mL of THF. For all cases, the concentrations of AM and AIBN were held constant at 0.5 and 5  103 mol/L, respectively. Diosgenin concentration was fixed at 0.01; 0.02 and 0.03 mol/L, while in another experience this steroid was replaced by cholestanol (CTN) [(3b,5a)-cholestan-3-ol] at a concentration of 0.03 mol/L. After purging de system with a current of nitrogen during 25 min, the solutions were introduced as soon as possible into the dilatometer, which was immediately sealed off. Then, the dilatometer was placed in a constant temperature bath at 50 °C (±0.05) as the chronometer was turned on. A cathetometer (±0.05 mm) was used for reading the heights of the liquid in the capillary until polymer precipitation.

2.1. Materials and methods

2.2. Theoretical models and methods

Diosgenin (commercial grade) was obtained from the Laboratorio Farmacéutico Mario Muñoz in Havana, Cuba; it was recrystallized before used in ethyl alcohol and dried under vacuum. Acrylamide and cholestanol (>90%) was purchased from Fluka. Benzoyl peroxide (BPO) was purchased from BDH; tetrahydrofuran (THF) (with no peroxides), and 2,2-Azobis(2-methylpropionitrile) (AIBN) were purchased from Merck. Both initiators were recrystallized in methanol and dried under vacuum. For all uses, water was bidistilled. 1H and 13C NMR spectra were recorded in a Brucker AC 250F at 250 MHz for 1H and 62.89 MHz for 13C.

Theoretical methods were employed to model the mechanism of the polymerization of AM in presence of DGN. In order to afford the computational cost, smaller polyatomic systems were considered keeping the structural zone of interest in every reaction (Fig. 2). DGN was simulated employing two molecules. One of them considers the A and B rings and includes the methyl group in C10. The other includes the ketal group with ring D. The methyl group at 21 and carbons 24, 25 and 27 from pyrane ring were removed. Methyl 19 remained because it is axial to both rings and could exert steric hindrance in a b face attack, contrary to methyl 21, which was removed because it is equatorial. It has a little influence on the radical attack to H16. Polyacrylamide radical was limited to one structural unit, i.e. propanoamide radical, where the higher spin density must be located at the more substituted carbon (Ca). We neglected the influence of the radical chain length on its reactivity (penultimate and antepenultimate effects). Some investigations focusing this problem have pointed out that there is not a general tendency on the dependence of rate coefficients with the number of structural units [19,20]. In spite of these approximations, the considered models can provide a qualitative picture of the polymerization processes. Radical attacks to vinylic systems were always oriented to the less substituted carbon, taking into account the general tendencies from theoretical and experimental studies [20,21]. Addition reactions involving the steroidal skeleton were modelled by addressing the attack to a face to avoid steric interactions with methyl 19. For hydrogen abstraction reactions, axial hydrogen atoms were favoured. The p bonding orbitals of the vinylic system lie parallel to the r antibonding orbital of the axial CAH; this bond is particularly weakened by effective orbital overlapping. All calculations were performed with the Gaussian 03 software package [22], within the Khon-Sham’s DFT routines. The unrestricted B3LYP hybrid functional on the 6-31G(d,p) basis set grounds was used in all geometry optimizations, location of

Fig. 1. Structure of diosgenin (DGN) and cholestanol (CTN).

2.1.1. Copolymerization A mixture of 2.25  102 mol of AM, 2.5  103 mol of DGN and 0.1  103 mol of BPO was dissolved in 5 mL of THF in a round bottom flask. The solution was purged with a current of nitrogen for 25 min. Immediately after, a refluxing condenser with the top covered by a balloon was attached to the flask and placed in a constant temperature bath during 5 h at 70 °C. Afterwards, the resulting white solid (S1) was filtered at low pressure, washed three times with 1 mL of fresh THF and dried under vacuum. The filtered THF solution was rotoevaporated and the crystalline solid obtained (S2) was dried under vacuum. S1: 1H NMR (D2O): d = 1.60–1.70 (broad, ACH2A of PAM), 2.15– 2.27 (broad, ACHA of PAM), 5.76 and 6.20 (m, vinylic H of AM). 13 C NMR (D2O): d = 35.00–36.17 (broad, ACH2A of PAM), 42.04 (broad, ACHA of PAM), 128.86 and 129.81 (vinylic C of AM), 178.83 (ACONH2 of AM), 179.86 (broad, ACONH2 of PAM). S2: 1H NMR (CDCl3): d = 0.81–1.04 (angular methyl groups of DGN), 3.40–3.56 (broad, 2H26 and H3 in DGN), 4.43 (m, H16 in DGN), 5.36 (d, H16 in DGN), 7.49–8.14 (protons of BPO). 13C NMR (CDCl3): d = 14.55–66.86 (backbone of DGN), 71.79 (C3 in DGN), 80.88 (C16 in DGN), 109.38 (C22 in DGN), 121.47 (C6 in DGN), 128.46–133.61 (BPO carbons), 140.77 (C5 in DGN).

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Fig. 2. Molecular models used in the calculations for PAM (top) and DGN (botton).

transition states, vibrational frequency calculations, scans of potential energy surfaces (PES) and intrinsic reaction coordinate (IRC) followings. This method and/or basis set have been widely employed [9–11,18,23,24] since geometry is not very sensitive to the method/basis set for free radical reactions [11,25]. Starting from the optimized geometry, the electronic energy of each molecule was recalculated at MPWB1K/6-31G(d,p) level. This methodology has been tested against experimental data and proved to yield more reliable kinetic results [10,11,13,17]. Moreover, we verified that optimized geometries obtained at B3LYP/6-31G(d,p) and MPWB1K/6-31G(d,p) do not differ in an important way and all relevant geometric features are kept with both functionals. MPWB1K is an hybrid meta functional developed by Zhao and Truhlar [26] that provides good performances for a combination of thermochemistry, thermochemical kinetics, hydrogen bonding and weak interactions, especially for thermochemical kinetics and noncovalent interactions. The functional was specified by using ‘‘MPWB95” with ‘‘IOP(3/76 = 0560004400)” in the keyword line. One dimensional conformational analyses were carried out by exploring the local PES at intervals of 30°, followed by full optimization of minima. Each maximum in the curve was optimized to a transition state (TS). Energy conformers and rotational barriers were reported taking into account the unscaled zero point vibrational energy (ZPVE). For B3LYP/6-31G(d,p) level the frequency scale factor for ZPVE corrections is 0.9806 [27]. It changes the energy barriers in no more than 0.2 kJ/mol. Hence, this refinement was neglected since during calculations we introduced models and approximations that must be more significant in the computations than frequency scaling. IRC calculations were done to find the connection between reactants and products through the corresponding transition states [28]. In all cases, transition states were characterized by a single imaginary frequency. Full conformational searching of products from the addition reactions was ruled out at this level of theory due to the size of adducts. Geometries and frequencies of products were computed from the full optimization of the last structure obtained in the IRC calculations. Rate coefficients were calculated according to the Transition State Theory (TST) by means of the Eyring equation for a bimolecular reaction [29]

k¼j

kB T RT Q – Q TS expðD– Eð0 KÞ=RTÞ h ph Q reac

ð1Þ

where j is the tunnelling correction factor, kB is Boltzmann’s constant, h is Planck’s constant, T is the thermodynamic temperature, R is the universal gas constant, ph is the standard pressure (1 atm), Q accounts for the total molecular partition function of reactants and transition state, while D–E (0 K) is the energy barrier with ZPVE correction for the reaction at 0 K, defined as the energy difference between the TS and the reactants. Expression (1) can be transformed as a function of Gibbs energy of activation D–G (defined as the difference between Gibbs energy of transition state and reactants) through

k¼j

  kB T RT exp D– G=RT h ph

ð2Þ

Tunnelling correction factors were estimated by means of the Wigner empirical expression [30]

jðTÞ ¼ 1 þ

1  mi  2 1:44 24 T

ð3Þ

where mi is the TS imaginary frequency (expressed in cm1), and T the thermodynamic temperature. More refined treatments of this factor require too long CPU times for systems of this size [31,32]. The rate coefficients were calculated for different temperatures. Arrhenius parameters were obtained for the temperature interval of 298–353 K by linear regressions of

ln k ¼ ln A  Ea =RT

ð4Þ

where A is the preexponential factor and Ea is the activation energy. The stabilization energies of the hydrogen bonding interactions present in some TS structures were calculated by applying the supermolecular approach at the same level of theory employed in kinetic determinations. Starting from the optimized TS geometry, we removed all atoms but those involved in the interaction and vacant valencies were fulfilled with hydrogens, while coordinates defining hydrogen bond geometry were frozen. The rest of the coordinates of the new system was then relaxed. Finally, the two separate fragments were fully relaxed, and the energy difference was assumed as the stabilization energy due to hydrogen bonding interaction. The effect of solvent was evaluated by employing a Polarizable Continuum Model (PCM) [33], in which the solvent is treated as an infinite polarizable dielectric medium of dielectric constant e, with

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the solute placed within a cavity inside this medium. Starting from the in vacuo optimized structure, solvation free energies DGsolv with non electrostatic effects was calculated at MPWB1K/6-31G(d,p)// B3LYP/6-31G(d,p) level employing THF (e = 7.58) as solvent at 323.15 K. The total free energy of each species in solution was calculated as

GTHF ¼ Ggas þ DGsolv þ RT lnð26:51Þ

ð5Þ

where Ggas accounts for the free energy in gas phase and RT ln(26.51) is a correction term at 323.15 K since Ggas were obtained for a reference state of 1 atm, while the solvation energy is computed for a reference state of 1 M [34]. 3. Results and discussion 3.1. Copolymerization The experimental approach was focused on the elucidation of the kinetic effects exerted by DGN on the AM homopolymerization and the possible copolymerization by cross addition between both compounds. Fig. 3 shows the NMR spectra of the fraction collected from the THF phase after polymerization of AM in presence of DGN with BPO as radical initiator. This phase seems to be mainly DGN, since the characteristic signals of the steroid are present, either in the 1H or in the 13C spectrum. Of particular interest is the proton shift close to 5.4 ppm and 13C signals at 121.5 and 140.8 ppm because

they reveal the presence of the double bond in C5AC6, suggesting that there is not at least an important presence of the AM and DGN oligomers in THF phase due to a copolymerization process. Moreover, there are peaks showing a clear aromatic pattern, which could be assigned to compounds formed during thermal homolysis of BPO. NMR spectra for the insoluble phase in THF are depicted in Fig. 4. Proton signals are clearly broad, which is consistent with the presence of polymeric molecules. Shifts in the region between 1.4 and 2.4 ppm could be assigned to the aliphatic hydrogens of PAM, while the small signals centred in 5.8 and 6.2 ppm can be attributed to the vinylic protons of the monomer trapped in the polymer. It is noticeable the absence of signals corresponding to DGN, which is confirmed if we take a look to the simplicity of the 13C spectrum. The aliphatic carbons of the polymeric chain (35.0 and 42.0 ppm) and the carbonylic nuclei of the amide groups (180 ppm) are visible. Hence, we noticed that NMR spectroscopy results support the absence of a cross addition step during radical homopolymerization of AM in presence of DGN, i.e., the vinylic bond in the steroid do not support copolymerization between AM and DGN. 3.2. Transfer reactions Given that transfer reactions do reduce the molecular weight of polymers, we performed viscosimetric measurements of isolated polyacrylamide (PAM) and polyacrylamide in presence of DGN (PAM–DGN). Calculated intrinsic viscosities [g] were then

(a)

(a)

(b)

(b)

Fig. 3. RMN spectra of the soluble THF phase: (a) 1H and (b)

13

C.

Fig. 4. RMN spectra of the insoluble THF phase: (a) 1H and (b)

13

C.

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used to compute the molecular weights from the Mark-Houwink equation

½g ¼ KMa with K = 6.5  103 mL/g and a = 0.82 for polyacrylamide [35]. PAM sample has a molecular weight of 7.1  104 Da, while PAM–DGN sample has a molecular weight of 4.7  104 Da. Since both polymers were synthesized in the same conditions, this noticeable decrease could be explained if DGN behave as a transfer agent in radical polymerization of AM. The next step was a dilatometric study to assess the kinetic effect of the transfer reaction on the AM homopolymerization. DGN content in the reaction mixture was varied as the AM concentration was held constant. In one of the experiments DGN was substituted by cholestanol (CTN, see Fig. 1) in order to define the structural region of diosgenin that acts during transfer process. The variation of the capillary height with time for different contents of DGN in the reaction mixture is shown in Fig. 5a. There is a very good linear correlation for every data set, showing zero order kinetic behaviour in the specified time interval. It is possible to relate the slope of the curves to the initial polymerization rate. The polymerization rate decreases as the DGN content is higher; this behaviour allow us to state that DGN acts as a retarding agent in the acrylamide polymerization. On the other hand, the slope of the linear correlation for the CTN (6%, mol-%) dilatometric data is similar to the slope for pure AM polymerization (Fig. 5b). Then, CTN is not a retarding agent of the acrylamide polymerization.

This different behaviour for both steroids seems to be associated to their different structures. DGN has a double bond between C5AC6 atoms and its side chain has a spiroketal structure. CTN does not have insaturations and it has an alkyl chain as substituent in ring D. Subsequently, the effects of both structural features in the kinetics of radical acrylamide polymerization were examined by computational methods. 3.3. Theoretical calculations The modelled reactions are depicted in Scheme 1 (Cartesian coordinates of all optimized structures, either minima or transition states, are available in Section A of Supporting information). HP and CP refer to addition reactions of propanoamide radical to acrylamide and diosgenin, accounting for typical homopropagation and copolymerization steps, respectively. Abstraction reactions in diosgenin steroidal zone (AS) was addressed to a hydrogens with respect to the double bond (C4 or C7), since the formation of an allylic radical helps these reactions. In order to model the abstraction reaction in diosgenin spiroketal side chain (AK), the H16 was considered because of the possible release of steric compression during radical formation and the ease of breaking this CAH bond given by the interaction between the nonbonding electrons in the furanic oxygen with the r antibonding orbital [36]. Finally, the last three reactions deal with the reinitiation step by addition of more favoured radicals to acrylamide monomer. Conformational minima of acrylamide and propanoamide radical were obtained by varying the dihedral angle CbCaCcN; the resulting one dimensional potential energy scans and the

(a)

(b)

Fig. 5. Dilatometric curves for AM polymerization in different conditions: (a) varying DGN (mol-%) content in the reaction mixture and (b) in presence of CTN compared with PAM blank and PAM with the same amount (in mol-%) of DGN.

Fig. 6. 1-D potential energy scan profile at B3LYP/6-31G(d,p) level by varying the dihedral angle u (CbCaCcN) of: (a) acrylamide and (b) propanoamide radical. Optimized geometries at B3LYP/6-31G(d,p) level of relevant conformers and rotational transition states are also shown.

O.F. Odio et al. / Journal of Molecular Structure 985 (2011) 34–47

39

Scheme 1. All reactions modelled (letters in boldface refer to compound codes and italics are related with the reaction series).

optimized structures of minima and rotational transition states are shown in Fig. 6 (detailed information is given in Table B1 of Supporting information). Acrylamide presents a planar conformation (1t) and other two equivalents (1e) where NH2 group lies 22.6° below and upon the vinylic bond. Propanoamide radical has two planar conformers, one with the NH2 anti to the CH3 (2t), and the other where both groups are eclipsed (2e). Rotational barrier for acrylamide appears lower than that of the radical. Nevertheless, at the reaction temperature (323 K), the interconversion must be fast enough to allow equilibrium between 2t and 2e. Both conformers were considered

for reactions involving propanoamide radical. In those reactions where acrylamide acts as reactant, 1t was only analyzed, since it is reported that the configuration of a b substituent in vinylic systems has little influence on the kinetics of radical attack to the alpha carbon [20]. The model compounds for diosgenin are represented in Fig. 7. In 3, ring A is in chair conformation and ring B adopts a half chair one because of the couple of trigonal carbon atoms. The isomer 4 was the only one used as a second model. In principle, rotation about dihedral angle OFC22OPC26 is allowed, but C22, C23, C26 and OP belong to the same pyranic ring provided that the real ketal is a spiro

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Fig. 7. Optimized geometries of diosgenin models 3 and 4 at B3LYP/6-31G(d,p) level.

compound; hence, any other conformation concerning the C22AOP single bond is not possible. With regard to the conformation of the spirocycle, furanic oxygen (OF) was located axial to the pyranic ring and pyranic oxygen (OP) was also placed in axial position to the furanic ring due to a double anomeric effect exerted by both oxygen atoms [37]. The trans junction between D and furanic rings locks the conformation as well. Table 1 shows calculated thermodynamic parameters of all reactions modelled at 323.15 K with MPWB1K/6-31G(d,p) //B3LYP/6-31G(d,p) level. Letters t and e denote that 2t or 2e was used respectively as propanoamide radical conformation. Homopolymerization appears more exothermic than copolymerization. This is consistent with the formation of a more stable adduct radical in the former reaction. The optimized structures of the adduct radicals are shown in Fig. 8. The acrylamide radical dimer 5 is planar, which facilitates overlapping between the unpaired electron and the p system of the amide group. The cross addition adduct 6 is a tertiary pyramidal radical since the value of the dihedral angle u (C10C4C6C5) is -15.3°. Pyramidalization hampers the radical stabilization due to hyperconjugation Table 1 Thermodynamic properties at 323.15 K of modelled reactions (MPWB1K/6-31G(d,p) //B3LYP/6-31G(d,p) level).

a b c

Reaction

DrHa (kJ/mol)

DrSb (J/mol K)

DrGc (kJ/mol)

HPt HPe CPt CPe AS4t AS4e AS7t AS7e AKt AKe RS4 RS6 RK

111.7 109.8 60.4 69.0 20.6 24.0 44.4 47.8 5.5 2.1 43.0 46.8 118.4

197.1 185.6 179.4 186.0 17.2 10.6 12.8 6.3 7.3 0.7 185.2 190.0 189.1

48.1 49.8 2.5 8.9 26.2 27.4 48.6 49.8 3.2 1.9 16.8 14.6 57.2

Reaction enthalpy. Reaction entropy. Reaction Gibbs free energy.

with r bonds. The distortion of the planar geometry is caused by the presence of substituents around the radical belonging to fused rings and by the gauche interactions arising from the new r bond between Ca of 2t and C6 of 3. HP is also favoured by the hydrogen bond formation between a carbonylic oxygen and a NH2 hydrogen (d(C@O  HAN) = 2.063 Å). The abstraction of hydrogen belonging to a carbon adjacent to the double bond C5AC6 in the diosgenin steroidal region is exothermic regardless the particular site of the radical attack. The resulting allylic radicals 8a and 8b (Fig. 9, top) are stabilized by electron delocalization. Table 2 shows the calculated geometric and electronic features of the allylic region. The interatomic distances between carbons forming the allylic system are similar and Mulliken spin densities are symmetrical around the central carbon. The unpaired electron is delocalized between the three centres due to its interaction with the adjacent p bond. Delocalization is effective due to the coplanarity of involved carbon atoms (note the small dihedral angle of the p system). The spin densities on the outer carbon atoms are similar. Then, further radical reactions concerning 8a and 8b will involve one of those atoms. The enthalpy differences between AS4 and AS7 can be explained taking into account the different stability of the particular radical formed. 8b is more stable than 8a. For the latter, A and B rings adopt half chair conformations. However, in the former the three trigonal carbons lie at the same ring, which has a flattened strained geometry, while ring A preserves a more stable chair conformation. Unlike hydrogen abstraction reactions involving the steroidal region, the propanoamide radical attack to H16 appears slightly endothermic. The radical product 9 (Fig. 9, botton) is somewhat bent (u (C17C15OFC16) = 28.9°) to allow overlapping of the halfoccupied orbital with one of the furanic oxygen’s lone pairs [38]. This interaction is reflected in a decrease of the C16AOF bond length while passing from 4 (1.436 Å) to 9 (1.382 Å). As a general trend, homopropagation and hydrogen abstraction from the diosgenin steroidal zone are fairly thermodynamically favoured, while hydrogen abstraction involving the spiroketal chain is unfavourable and cross addition of acrylamide radical to diosgenin double bond is slightly exergonic. 3.3.1. Transition states: rate coefficients Table 3 shows classical reaction barriers, empirical Arrhenius parameters and rate coefficients for each reaction computed at B3LYP/6-31G(d,p) and MPWB1K/6-31G(d,p)//B3LYP/6-31G(d,p). A comparison of the kinetic results obtained with both functionals shows that the more reliable MPWB1K gives lower energy barriers for addition reactions, while energy barriers for hydrogen abstractions seems to be less sensitive when passing from B3LYP to MPWB1K, though the former slightly yields higher barriers when the abstraction comprises the steroidal region. In spite of these variations, it is noted that the general trend in the order of reactivity is not altered. Fig. 10 shows optimized structures of the transition states corresponding to HP and CP reactions. As was expected from the Hammond postulate, the more exothermic the reaction, the earlier the transition state. Thus, the forming r CAC bond distance is larger for homopropagation than for cross addition; similar considerations apply for the stretching of the double bond, which is greater for TS(3) and TS(4) than for TS(1) and TS(2). The large difference in energy barriers can be explained if we consider that in HP the attacked alkene’s carbon is unsubstituted, while in CP the attacked alkene’s carbon has a substituent that hinders the approach of propanoamide radical. Besides, the substituent in C5 belongs to a cyclic structure; hence, rehybridization of C5 from sp2 to sp3 is more difficult than for acrylamide monomer. It is noticed the presence of a hydrogen bond in both TS(1) and TS(2) between a carbonylic oxygen and one of the amide’s

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Fig. 8. Optimized geometries of addition products 5 and 6 (bond distances are in Å) at B3LYP/6-31G(d,p) level. On the right, a detailed zone around the fused rings showing the pyramidal structure of the radical.

Fig. 9. Optimized geometries at B3LYP/6-31G(d,p) level of radicals produced by hydrogen abstraction from diosgenin. Top: 8a and 8b; bottom: 9.

Table 2 Mulliken spin densities, geometric parameters of the allylic system and relative energy for abstraction products in diosgenin steroidal zone at B3LYP/6-31G(d,p) level. Product

Er (kJ/mol)

Allylic bond distance (Å)

Dihedral angle of the p system (°)

Mulliken spin density

8a

20.9

C4AC5 1.395

C5AC6 1.393

u (C6C5 C4 H4) 4.2

C4 0.65

C5 0.26

C6 0.64

C5AC6 1.395

C6AC7 1.386

u (C5C6 C7 C8) 1.1

C5 0.64

C6 0.26

C7 0.64

8b

0

hydrogens. The optimization of the hydrogen bond portion of the transition state structures yielded stabilization energies of 5.2 and 1.3 kJ/mol for TS(1) and TS(2) respectively, which is consistent with the smaller distance ANH  O found in TS(1) compared with that found in TS(2). Hydrogen bond formation during HP could contribute to the differences in reactivity between this monomer and diosgenin double bond toward polyacrylamide radical addition. Indeed, stabilization energy difference by means of hydrogen bond formation in TS(1) and TS(2) seems to play a major roll in the discrepancies encountered between reaction barriers of HPt and HPe (ca. 5 kJ/mol). According to these results, CP reactions are slower than HP in several orders of magnitude (kCP/kHP  105). Polyacrylamide radical would add to an acrylamide molecule with much more probability than to a diosgenin molecule, which is in agreement

with spectroscopic results shown in Section 3.1. Therefore, addition of AM to DGN as a copolymerization step appears to have no influence on the kinetics of retardation in acrylamide homopolymerization. Fig. 11 shows optimized transition state structures along with the L value corresponding to the six hydrogen abstraction reactions that would take place using both 3 and 4 as reactants (Table B2 of the Supported information summarizes the main geometric features for these transition states). Parameter L is used to analyze the position of the TS in the reaction coordinate (if L < 1, the TS is considered earlier) [18], and is calculated for these particular abstraction reactions as

L¼

dðCX AHÞTS  dðCX AHÞreact lðCa    HÞTS  lðCa    HÞproduct

ð6Þ

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Table 3 Kinetic parameters of modelled reactions at two levels of theory (temperature: 323.15 K). Reaction

Log Ae

a

B3LYP HPt HPe CPt CPe AS4t AS4e AS7t AS7e AKt AKe RS4 RS6 RK a b c d e f

5.3 5.6 5.5 5.5 5.7 5.8 6.9 6.5 5.3 5.8 5.6 5.5 5.3

Ead (kJ/mol)

DE–(0 K)c (kJ/mol)

15.7 21.4 53.9 49.2 43.1 26.7 41.3 36.0 38.1 40.5 53.9 52.1 4.7

b

MPWB1K 9.3 14.0 38.5 32.4 44.1 27.1 43.7 40.4 35.7 39.9 45.3 42.6 0.5

B3LYP 17.6 23.5 57.9 53.5 43.4 27.5 43.4 37.6 38.6 42.2 57.4 55.5 8.3

a

kf (L/mol s) MPWB1K 11.2 16.2 42.6 36.6 44.4 28.0 45.8 42.1 36.2 41.6 48.8 46.0 4.2

b

B3LYPa

MPWB1Kb 2

2.6  10 6.5  101 1.4  104 6.8  104 5.0  102 2.1  101 7.3  101 2.5  100 1.1  101 1.1  101 2.3  104 3.2  104 9.8  103

2.9  103 1.0  103 4.1  102 3.7  101 3.5  102 1.7  101 3.0  101 4.8  101 2.8  101 1.3  101 5.6  103 1.1  102 4.6  104

B3LYP/6-31G(d,p) level. MPWB1K/6-31G(d,p)//B3LYP/6-31G(d,p) level. Reaction barrier at 0 K corrected for ZPVE. Activation energy calculated by regression of Eq. (4). Preexponential factor calculated by regression of Eq. (4). Rate coefficient calculated according to Eq. (2).

Fig. 10. Optimized geometries of TS(1)–TS(4) at B3LYP/6-31G(d,p) level (bond distances are in Å).

where dðCX AHÞ is the bond length between C4, C7 or C16 and the abstracted hydrogen atom, while lðCa    HÞ is the distance from this atom to the radical centre Ca in propanoamide radical. The more exothermic the reaction, the earlier appears the transition state. Indeed, L is close to unity for abstraction in the spiroketal chain, where the reaction is endothermic. The near to co-linear arrangement of the three centres involved in the abstraction indicates that the hydrogen atom is sterically accessible for the radical attack. The attack in C4 is more hindered probably due to the methyl group in C10. Reaction AS4 becomes the dominant abstraction process due to its smaller activation energy with respect to the other abstraction reactions; this could be related to the hydrogen bond formation in TS(6) between the carbonylic oxygen of the attacking radical and

the hydrogen of the diosgenin hydroxyl group. The stabilization energy for this interaction is about 11 kJ/mol. The N  HAO interaction in TS(5) was investigated. This interaction destabilizes the transition state around 6 kJ/mol. These results explain the differ– ences between DE– 5 and DE6 . In contrast, stabilization energy due to the hydrogen bond NAH  O involving an amidic hydrogen and pyranic oxygen (9.3 kJ/mol) in TS(9) is by far greater than the small energy barrier difference found between AKt and AKe. There are other factors that counteract the presence of hydrogen bond interactions. The calculated Wigner’s tunnelling correction factors at 323.15 K for the modelled hydrogen abstraction reactions showed little variation between 2.9 and 3.2 (Table 4). Although it is considered that this approach often underestimates the tunnelling effect

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O.F. Odio et al. / Journal of Molecular Structure 985 (2011) 34–47

Fig. 11. Optimized geometries of TS(5)–TS(10) and respective L values at B3LYP/6-31G(d,p) level (bond distances are in Å).

because it only includes contributions near the top of the barriers [32], it is important in the treatment since j(T) is assumed to be unity for addition reactions given that the corresponding imaginary frequency are small enough. Therefore, although activation energies for hydrogen abstraction reactions are similar to those of copolymerization steps at MPWB1K/6-31G(d,p)//B3LYP/6-31G(d,p) level, tunnelling effect as well as higher preexponential factors contribute to a resulting ratio P k /k not too small as in the case of cross addition, being P ABS HP kABS the sum of all abstraction reactions that take place in DGN. In other words, hydrogen abstraction reactions could compete with the homopropagation step and can be considered as effective transfer reactions. According to these results, the abstraction of a DGN hydrogen atom is not negligible. This reaction decreases the PAM molecular weight, in agreement with the experimental trend observed in Section 3.2. 3.3.2. Reinitiation reactions In order to analyze the influence of these hydrogen abstraction reactions on the overall kinetics of acrylamide polymerization, the reinitiation steps were also considered. The key magnitude is the rate at which radicals created by the transfer events add to a

Table 4 Wigner tunnelling correction factors (j) at 323.15 K calculated for hydrogen abstraction reactions.

a b

Reaction

ma (cm1)

jb

AS4t AS4e AS7t AS7e AKt AKe

1612.36 1579.73 1561.97 1554.25 1625.12 1520.76

3.15 3.06 3.02 3.00 3.19 2.91

TS imaginary frequency at B3LYP/6-31G(d,p) level. Calculated according to Eq. (3).

new monomer. Two reinitiation steps were considered, one with radical 8a produced in the diosgenin steroidal zone and the other with radical 9 belonging to the spiroketal chain (see Scheme 1). Moreover, addition of 8a to acrylamide monomer was split into two reactions (RS4 and RS6) since C4 and C6 atoms have similar spin densities. Calculated thermodynamic and kinetic parameters are shown in Table 1 and 3. Optimized structures of modelled transition states are shown in Fig. 12.

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O.F. Odio et al. / Journal of Molecular Structure 985 (2011) 34–47

Fig. 12. Optimized geometries of TS(11)–TS(13) at B3LYP/6-31G(d,p) level (bond distances are in Å).

Reinitiation from radical 9 is highly exothermic and takes place with very low activation energy. The rate coefficient is even greater than that of homopropagation. The interaction between an electron donor substituted radical like 9 and an electron withdrawing substituted alkene like 1 increases the reaction rate due to a partial electron transfer in the transition state from the radical to the alkene. Previous pyramidalization in 9 contributes to an early transition state, reflected in a longer CAC distance between the radical centre and the unsubstituted trigonal carbon in acrylamide [20]. Reinitiation concerning radical 8a is not thermodynamically favoured and it is several orders of magnitude slower with respect to acrylamide homopolymerization. Its low exothermicity (compared with other additions) arises as a result of the resistance to rupture of the stabilized allylic system to form the new radical. Reaction barriers are relatively high to overcome the resonance stabilization in the initial radical and to allow the pyramidalization of the transition state. This is reflected in the geometry of TS(11) and TS(12), where the forming CAC bond is shorter than for TS(13) and the rupture of the allylic geometry is obvious. It can be noticed that addition of acrylamide to radical 8a is somewhat regiospecific, since the rate coefficients for addition in C4 is half the rate coefficient for addition in C6. Small differences in energy barriers are related to a shift in the hydroxyl group of the ring A from an equatorial to a less favoured axial position during the pyramidalization of 8a when the radical attack involves C4 (see TS(11)). In the case of the radical attack concerning C6, pyramidalization of 8a does not influence the conformation adopted by ring B because C7 has no substituents (see TS(12)). Based on these results, we can suggest that reinitiation from radical 9 would not influence the overall kinetics of acrylamide

polymerization, since the formation of the new radical is fast enough to keep constant the radical concentration; however, reinitiation from the radicals formed during abstraction in the diosgenin steroidal zone is quite slow if compared with the propagation step. Hence, a net depletion of radical concentration would occur, which must effectively account for a reduction of the polymerization rate. The results for all processes can be summarized in the reaction profiles represented in Fig. 13. 3.3.3. Solvent modelation In order to take into account the solvent effect since experiments were achieved in solutions of THF, the kinetics of some relevant reactions was studied using PCM. We did not find any report in the literature where this solvent exhibited an important protic behaviour; thus, THF was considered an aprotic solvent for which the continuum model seems to be acceptable. Table 5 shows the estimated kinetic parameters at 323.15 K in THF phase and a comparison with the calculated parameters in gas phase. It can be noticed that preexponential factors increase in one order of magnitude for all reactions considered, which could be associated with a decrease in the solvation degree from reactants to transition state, leading to a positive increment of the entropy. On the other hand, there is an increase of the activation energy from gas to solution, which confirms that the reactants are more affected by the solvent than the transition states. This effect is more pronounced for homopropagation and hydrogen abstraction in the steroidal zone, where the transition state structures show hydrogen bonds. It suggests that THF solvent field does not stabilize this interaction.

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O.F. Odio et al. / Journal of Molecular Structure 985 (2011) 34–47

Fig. 13. General energy profile at 323 K of the modelled reactions at MPWB1K/6-31G(d,p)//B3LYP/6-31G(d,p) level. Values of DGr and DG– are in kJ/mol. HP: homopolymerization; CP: cross propagation; AS: hydrogen abstraction in the steroidal zone; AK: hydrogen abstraction in the spiroketal moiety; RS: reinitiation step from a steroidal radical; RK: reinitiation step from a spiroketal radical.

Table 5 Energy barriers and Arrhenius parameters calculated at 323.15 K for some selected reactions in THF solution using PCM and their comparison with gas phase (GP) results (MPWB1K/6-31G(d,p)//B3LYP/6-31G(d,p) level).

a b c

Reaction

a (kJ/mol) ETHF a

Log ATHFb

kTHFc (L/mol s)

 EGP ETHF a a (kJ/mol)

ATHF/AGP

kTHF/kGP

HPt AS4e CPe RS6

22.7 41.1 45.6 50.8

7.12 7.63 7.35 7.33

2.8  103 9.7  100 9.3  101 1.3  101

11.5 13.1 9.0 4.8

22.6 21.0 21.8 21.9

1.0 0.6 2.5 11.8

Activation energy calculated by regression of Eq. (4). Preexponential factor calculated by regression of Eq. (4). Rate coefficient calculated according to Eqs. (2) and (5).

of TS(1) and TS(6) after re-optimization using PCM with THF. It is apparent that for TS(1) the forming CAC r bond has become shorter in more than 0.01 Å, while the hydrogen bond interaction appears extended in 0.03 Å with respect to the gas phase (cf. Fig. 10). Similarly, the hydrogen bond in TS(6) is elongated in almost 0.04 Å (cf. Fig. 11); the parameter L (defined in Eq. (6)) is now shifted from 0.688 to 0.716, denoting a later transition state in solution. As a result of the balance between activation energy and preexponential factor effects, rate coefficients for selected reactions do not show large variations when going from gas to solution phase, which is consistent with previous studies [11,12,39] where the solvent does not present specific interactions with the solutes considered. This is true except for the reinitiation step, which is accelerated in one order of magnitude. However, as we are interested in the ratio of the rate coefficients for a qualitative analysis of the behaviour of the system, we observe from Table 6 that there are not substantial differences in the relative ratios for gas and solution phases. It is important to remark that PCM study corroborates the general trends observed in the gas phase calculations. It means that environmental solvent molecules are not influencing if they do not participate exchanging protons or any other reactive site by themselves. Table 6 Ratios of rate coefficients calculated at 323.15 K for gas phase and in THF solution (PCM) modelations (MPWB1K/6-31G(d,p)//B3LYP/6-31G(d,p) level). Fig. 14. Optimized geometries at B3LYP/6-31G(d,p) level of TS(1) and TS(6) in THF phase using PCM as solvation model (bond distances are in Å).

The increase in the activation energy is consistent with a later transition state geometry. Fig. 14 shows some geometric parameters

Kinetic ratio

Gas phase

THF solution

kCPe/kHPt kAS4e/kHPt kRS6/kHPt

1.3  104 5.9  103 3.8  106

3.3  104 3.5  103 4.6  105

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O.F. Odio et al. / Journal of Molecular Structure 985 (2011) 34–47

Scheme 2. Proposed mechanism for the retardation of acrylamide polymerization in presence of diosgenin.

All results and considerations can be summarized in the following mechanistic scheme (Scheme 2) that explains the retardation of acrylamide polymerization in presence of diosgenin. The radicals produced by hydrogen abstraction (II) do not reinitiate the growing chain at significant rates compared to polyacrylamide radicals homopropagation (I), leading to self and cross termination (III). 4. Conclusions We built a theoretical model to explain qualitatively the polymerization process of acrylamide in the presence of an unsaturated steroid like diosgenin. The general conclusion is that the participation of the steroidal unsaturated segment explains the experimental behaviour. Two important features arise from these studies: copolymerization between AM and DGN is unfavourable and there are transfer reactions causing a retardation effect in the polymerization kinetics. The modelled thermodynamics and kinetics of studied reactions at the MPWB1K/6-31G(d,p)//B3LYP/6-31G(d,p) level of theory suggest that transference occurs mainly by a hydrogen atom abstraction from a carbon adjacent to the diosgenin double bond. The resulting allylic radical reinitiates polymerization at a very slow rate, which leads to retardation. The same trends are observed either in gas or in THF solution phase within PCM framework. These results show that diosgenin is not suitable for the synthesis of amphiphilic copolymers of acrylamide.

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Acknowledgements We acknowledge the Laboratorio de Productos Naturales from the Facultad de Química of Universidad de La Habana for diosgenin and cholestanol supplies. Computational studies were supported by the Universidad de La Habana (Cuba), the Universidad Autónoma de Madrid (Spain), and projects CTQ-63332BQU of MEC (Spain) and D/019558/08 of AECID (Spain). Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.molstruc.2010.10.006.

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