ISSN 1061-933X, Colloid Journal, 2017, Vol. 79, No. 5, pp. 577–587. © Pleiades Publishing, Ltd., 2017. Original Russian Text © P.O. Baburkin, P.V. Komarov, M.D. Malyshev, S.D. Khizhnyak, P.M. Pakhomov, 2017, published in Kolloidnyi Zhurnal, 2017, Vol. 79, No. 5, pp. 534– 543.
Computer Simulation of Structuring in Aqueous L-Cysteine–SilverNitrate Solutions under the Action of Initiating Salt P. O. Baburkina, P. V. Komarova, b, *, M. D. Malysheva, S. D. Khizhnyaka, and P. M. Pakhomova aTver
bNesmeyanov
State University, Tver, 170002 Russia Institute of Organoelement Compounds, Russian Academy of Sciences, Moscow, 119991 Russia *e-mail:
[email protected] Received August 1, 2016
Abstract⎯Structural transformations occurring in aqueous L-cysteine−silver-nitrate mixed solutions (CSSs) upon the addition of an initiating salt have been studied within the framework of mesoscopic simulation using the dissipative particle-dynamics method. Diffusion of silver mercaptide clusters is decelerated, and metastable chain aggregates thereof are formed in a narrow concentration range of the salt, probably due to the transition into a gel-like state. The results obtained are in qualitative agreement with the experimentally observed behavior of CSSs. DOI: 10.1134/S1061933X17050039
INTRODUCTION The great interest in the study of hydrogels (HGs) is due to their prevalence in the everyday life and wide use in technological processes [1–8]. The study of HGs is also of importance from the fundamental point of view, because the gel-like state is an interesting example of metastable systems, which can change and recover their structure under variable external actions. It has been suggested that insight into the factors that govern phase transitions in a solution that result in the formation of HGs, will make it possible to design new molecular assemblies capable of targeted self-assembly and desirable responses to changes in external factors [4, 7, 8]. On the basis of the nature of interparticle interaction, gels may be classified into chemical ones, in which the main factor for the formation of a spatial network is covalent bonding, and physical ones, the energy of which is comparable with thermal energy ~kBT (kB is the Boltzmann constant, and T is the absolute temperature) [6]. In this work, we employ computer simulation to investigate a molecular system prepared from aqueous L-cysteine and silver-nitrate solutions (CSSs). This system can form biocompatible physical supramolecular HGs at low concentrations of the reagents on the order of 0.01% [9–11]. Previous experimental studies of CSSs [9–12] have shown that, when cysteine and AgNO3 solutions are poured together, silver mercaptide (SM) zwitterions are formed via the substitution of hydrogen atoms in thiol groups by silver atoms. The gel-like state arises in CSSs during aging after the addition of various salts that dissociate to yield both singly and doubly charged
anions and metal cations. The stage of aging lasts from 28 min to 48 h depending on temperature. Positively charged SM aggregates (which further play the role of supramonomers) with different radii of inertia (1– 600 nm) are, at this stage, formed in the solution, as can be seen from dynamic light-scattering and potentiometry data [10, 12]. Moreover, their formation has been investigated by computer simulation [13–16]. According to full-atom molecular-dynamics data [14–16], SM aggregates may form fiberlike structures via hydrogen bonding between free C(O)O– and NH 3+ functional groups on their surfaces. The possibility of such self-assembly of supramonomers into the fibers of a gel network is indirectly confirmed by the fact that HGs are not formed in solutions based on cysteamine and mercaptopropionic acid [17]. These substances contain thiol groups; however, in contrast to cysteine, cysteamine has no carboxyl group, and there is no amino group in mercaptopropionic acid. Another indirect confirmation of the established mechanism is the self-assembly of silver and gold nanoparticles via cysteine molecules grafted onto their surfaces [17, 19]. Finally, in [20], we have simulated the formation of a gel network in terms of a mesoscopic model using a coarse-grained representation of SM zwitterions. The model has been developed taking into account the conclusions drawn in [14–16] concerning a possible mechanism for the self-assembly of SM zwitterions via carboxyl and amino groups. An equivalent simplified structure composed of four force centers was used as a model of SM, with two centers corresponding to NH 3+ and C(O)O– polar groups and other two centers
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reflecting nonpolar groups of SM zwitterions. Due to this structure, SM forms aggregates (colloidal particles), in which the nonpolar moieties of the molecules compose cores, while the polar moieties form the surface. The incorporation of a gelation-initiating salt was implicitly taken into account by varying the parameters of the interaction between cysteine C(O)O– and NH 3+ groups and a solvent. It has been shown that a narrow range, in which the system passes into the gellike state, may be found by means of gradual variations in the interaction parameters, with these variations in the model corresponding to variations in the salt concentration. This method, which was selected to take into account the presence of salt, has been supported by the results of works [21–23], in which it was shown that the addition of a salt led to a decrease in the number of hydrogen bonds per dissolved molecule. Although, the approach proposed in [20] for taking into account the action of the initiating salt at the mesoscopic level has appeared to be efficient, it has a significant drawback. The implicit allowance for the introduction of the salt via the parameters of the interaction between the polar groups of SM and the solvent entails a uniform distribution of salt ions in the bulk solution, which takes place only in the case of the electrostatic nature of intermolecular interactions in a system under an additional condition that the temperature is higher than the Manning threshold [24]. At optimum concentrations of HG components, i.e., cysteine, 3 mM; silver nitrate, 3.75 mM; and initiating salt, 0.25 mM [9, 10, 17], the Debye radius is equal to ≈46.7 and ≈48 Å in the presence and absence of an initiating salt, respectively. This indicates that the selfassembly in CSSs is not caused by the deterioration of the electrostatic stabilization of a solution, but has another reason. In our opinion, the self-assembly in CSSs at electrolyte concentrations as low as these may be explained by the fact that metal ions can form complexes with amino acids, which may also affect the character of the intermolecular interaction. Thus, to develop work [20], we intend an investigation of the ability of SM aggregates to self-assembly into a network with explicit allowance for the ability of SM zwitterions to form complexes with metal ions. Therewith, we do not take into account that SM aggregates may carry an electrostatic charge. It should be emphasized that this formulation of the problem entails the verification of the possibility of the selfassembly of supramonomers of SM molecules via the complexation of their functional groups with metal ions. MESOSCOPIC MODEL OF CSS AND THE DISSIPATIVE PARTICLEDYNAMICS METHOD To investigate structural transformations in CSSs upon the addition of an initiating salt, we employ a
modified coarse-grained model [20] based on the dissipative particle-dynamics (DPD) method [25–28]. The coarse-grained simulation enables us to decrease the calculation time for large volumes of a substance owing to the exclusion of a significant number of the degrees of freedom. In order to choose a method for taking into account the complexation of SM zwitterions with metal ions, we decided to perform a study of the coordination of cysteine functional groups with metal ions as a sublevel of the total investigation. For this purpose, we simulated the complexes of L- and D-cysteine with Na+ ions. SM complexes were constructed via the geometrical optimization of generated molecular systems within the framework of the density-functional theory (DFT) under the generalized gradient approximation (GGA) using the BLYP functional [29, 30] and DNP (double numerical plus polarization) basis [31, 32]. The calculations were performed under the conditions of vacuum and the total charge of the system equal to +1e. The initial position of a Na+ ion was preset in a random manner at a distance of 2–3 Å from C(O)OH, NH2, and SH functional groups of L- and D-cysteine in the molecular and zwitterionic forms. At the same time, the coordination of only the thiol group by the metal ion was not considered, because we proceeded from the assumption that only SM zwitterions were present in the solution. The following forms of coordination of the functional groups were considered. (1) Monodentate form: metal-ion bonding with a carbonyl oxygen atom (сys-1) (Fig. 1). (2) Bidentate form: bonding with a deprotonated carboxyl group (сys-2) via carbonyl oxygen and sulfur atoms (сys-3) and via nitrogen and carbonyl oxygen atoms (сys-4) (Fig. 1). (3) Tridentate form: metal-ion bonding between hydroxyl oxygen, nitrogen, and thiol sulfur atoms (сys-5) and via carbonyl oxygen, nitrogen, and sulfur atoms (сys-6) (Fig. 1). The systems resulting from the geometric optimization (examples of them for the case of L-cysteine are given in Fig. 1) were used for comparison of the energies of L- and D-isomers: ΔE = |E(cys-n) – E0|; (1) here, E(cys-n) is the energy of the optimal configuration of the cys-n complex (Fig. 1) and E0 is the energy of the cys-6 system. As follows from Fig. 2, L- and D-cysteine isomers form complexes with sodium ions, which are characterized by close values of bond energy. Therewith, metal ion may coordinate both individual functional groups and several groups simultaneously (Fig. 1), which is in good agreement with the results of [33]. Hence, cysteine and SM complexed with a metal ion will interact with water molecules in a somewhat different way than they interact with them when in the free state [21–23]. COLLOID JOURNAL
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N Na+
H
O C
S
Na+
Na+ Cys-1
Cys-2
Cys-3
Na+ Na+ Na+
Cys-4
Cys-5
Cys-6
Fig. 1. Optimized structures of L-cysteine complexes (cys-n, n = 1–6) with Na+ ion calculated within the framework of DFT.
Let us describe the principles of the formulation of the coarse-grained model of CSS. As in previous work [20], it is assumed that the formation of SM zwitterions has been completed in a solution, and the main parameters, which govern the behavior of the system, are the concentrations of SM and an initiating salt. To take into account the presence of the salt, we introduce SM zwitterions of two types, A and B, into the CSS model. Functional groups of type-A zwitterion are assumed to be coordinated by the metal ion. This hinders the hydrogen bonding with water and makes the groups less hydrophilic as compared to non-coor-
dinated type-B zwitterions. This circumstance can be taken into account by the appropriate choice of the parameterization of the intermolecular interaction. Thus, the model of CSS contains two types of SM zwitterions and a solvent. The amount of the added salt is controlled by the ratio between volume fractions (vol %) CA and CB of SM zwitterions using parameter f = CA/(CA + СB). SM zwitterions contain five spherical force centers (which are hereafter referred to as “particles”) conventionally denoted as O, N, С, S, and Ag. Water molecules are denoted as “W-type particles.” Note that the denotations of the model parti-
ΔE, kcal/mol 20 1 2
15
10
5
0 1
2
3
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6 Cys-n
Fig. 2. Relative energies of the complexes of (1) L- and (2) D-cysteine isomers with Na+ ion calculated within the framework of DFT, GGA approximation, BLYP functional, and DNP basis. COLLOID JOURNAL
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NH3+
COO–
A
B
O
P C
C
C N
H
H S
S
S Ag
Ag
Ag
Fig. 3. Transition from the full-atom model to coarse-grained models of SM zwitterion. The first model (type-A zwitterion) corresponds to the SM zwitterion−metal ion complex, while the second model (type-B zwitterion) represents uncoordinated SM zwitterion. Correspondence of the groups of atoms in the full-atom model to the equivalent coarse-grained representation is as follows: Ag → Ag, CH2S → S, С(O)O– → O (coordinated by metal ion) and P (uncoordinated), CH → C, and NH3+ → N (coordinated) and H (uncoordinated).
cles are conventional; their choice has been dictated by the convenience of the visualization programs, which operate with a fixed set of the denotations of chemical elements. The correspondence of the conventional symbols to the atomic groups is presented in the caption to Fig. 3. As before, the DPD method [25–28] is used for the simulation. In DPD, all particles have the same diameter σ = 1 and mass m = 1. The number-average particle density in the system is taken equal to three. DPD may be considered to be a mesoscopic version of the conventional molecular dynamics, because the evolution of the system is described by the following set of Newtonian equations:
d ri dt = v i and d v i dt = f i , fi =
∑
i≠ j
Fij'
Spr
+ Fij + Fij + Fij , C
R
Fij' Spr = C | rij − σ | ˆrij , r C Fij = aij (1 − ij ) rij , rc D D Fij = −γω (rij )(v ij ⋅ ˆrij )ˆrij ,
D
(2)
FijR = ξω R (rij )θ ij ˆrij , where ri is the radius vector, vi is the velocity of an ith particle, rij = rij | rij | is the unit vector drawn from particle j to particle i, C is the stiffness coefficient
equal to 4kВТ/σ2 (kBT = 1), ω D(rij ) and ω R (rij ) are weighting functions, γ = 4.5 τ–1 is the friction coefficient (here, τ is the characteristic time unit equal to σ m/ k BT ), ξ characterizes the magnitude of the thermal noise, and θ ij is a random value that has a normal distribution with a mean value and variance equal to zero and γkBT/τ, respectively. When calculating resultant force f i, the summation is carried out over all the particles inside the region bounded by the cutoff radius of the interaction rij ≤ rc = σ. Fij' Spr , FijC , FijR , and
FijD are the contributions from the following central forces: the force of deformation of the valence bond between coarse-grained particles and the conservative, random, and dissipative forces, respectively. In this case, Fij' Spr and FijC describe the intramolecular and intermolecular interactions, respectively. The prime symbol at force Fij' Spr means that only the contributions from particles bonded to each other are considered. The dissipative force describes the hydrodynamic friction, which decreases the particle energy. The random force returns the energy into the system, thereby compensating for the dissipative force; i.e., it ensures the fulfillment of the conservation laws. According to [26], weighting functions are usually specified as follows: (ω R (rij )) 2 = ω D(rij ) = (rc − rij ) 2. COLLOID JOURNAL
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In addition, it has been shown in [26] that the DPD system represents a canonical ensemble and obeys the fluctuation–dissipation theorem [34], which ensures the equilibration of the system at long times of simulation. Constants γ and ξ are interrelated as ξ2 = 2γkBT, thereby providing the response of the simulated system to a change in its energy (temperature). Because forces FijC are defined as linear functions of rij, the particles may overlap, thus significantly accelerating diffusion and phase separation in the system. Since all forces are paired and short-range ones, their sum is equal to zero, and the values of the momentum and the moment of the momentum remain preserved, the hydrodynamics of the liquid corresponds to the Navier–Stokes equation. The parameterization of the intermolecular interaction is performed on the basis of the fact that the Bjerrum length in an aqueous solution is ≈6.9 Å. This value is comparable with the molecular size of silver mercaptide. Since SM molecules in the CSS have the form of zwitterions (that is, they may be considered as dipoles with an arm length of ≈4 Å), the energy of the Coulomb interaction between two zwitterions exceeds the energy of the thermal motion only at small distances, at which they may be hydrogen bonded. Therefore, the electrostatic interaction is not taken into account in our model. The relationship of the coarse-grained particles with their real chemical structure is specified by force constants aij, which determine the amplitudes of the maximum repulsion of the particles. In the case of an aqueous solution, they are expressed via Flory−Huggins parameters χij by the following simple relation [27, 28]:
aij = 25 + 3.497χ ij k BT .
(4)
The values of χij govern the character of the interaction between particles of different types. When χij ≈ 0 (aij ≈ 25), the ith and jth particles may freely overlap. The value of χij may be calculated using the known relationship between the Flory–Huggins parameters and Hildebrandt solubility parameters δi [35]:
V ref (δ i − δ j ) 2 (5) , RT where Vref = 38.7 cm3/mol is the average molecular volume of the fragments for the chosen dividing of the SM (Fig. 3) and R is the gas constant. Set of motion equations (2) is integrated using the modified Verlet velocity method with step Δt = 0.05τ (τ is the unit of time) [36]. All calculations have been performed using the DPD_Chem program [39]. The solubility parameters of C, S, Ag, and W particles (δC = 35.0 kPa1/2, δS = 30.0 kPa1/2, δAg = 10.0 kPa1/2, and δW = 40.9 kPa1/2) have been calculated by the procedure described in [20]. Values of 40.0 kPa½, which χ ij ≅
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are close to δW, have been taken for the solubility parameters of P and H particles (uncoordinated zwitterions В). In the case of coordinated zwitterions A, δi values of 34.5 and 34.0 kPa1/2 have been selected for O and N particles, respectively, because macrophase separation occurs in the system in this case [20]. Taking into account the conclusions inferred in [37], the following interrelation between τ and real time will be 53 valid for the aqueous solution: τ = (25.7 ± 0.1) N w ps, where Nw is the number of water molecules corresponding to the volume of a DPD particle. Since, in our model, σ ≈ 0.27 nm, Nw = 6.5, which gives τ = 25.7 ± 2.3 ps. Thus, we have Δt ≈ 1.3 ps.
RESULTS AND DISCUSSION The behavior of CSS was studied using a cubic cell with edge length L = 32σ and periodic boundary conditions. Two main parameters were varied, namely, the volume fraction of SM СSM = СA + СB and the ratio between the fraction of type-A zwitterions and the total content of the dissolved substance in the cell, with this ratio being controlled by parameter f. An increase in f corresponds to a variation in the salt concentration in the solution, because the type-A particle corresponds to a zwitterion, in which the functional groups are coordinated by the metal ion. To test the developed model, we constructed three variants of the initial states of CSS with a random distribution of SM at different ratios between coordinated and uncoordinated SM zwitterions. The following values of the parameters were used: f = 0, 0.5, and 1 at fixed CSM = 2 vol %. As in [20], the total volume fraction of SM corresponded to the conditions of stabilized CSS [9–11]. At f = 0, the behavior of the constructed model corresponded to the absence of the initiating salt (ripe CSS), while, at f = 1, it corresponded to the macrophase separation in our previous model [20]. Test calculations have shown that, in the model CSS, SM clusters are readily formed, the number of which is stabilized at f = 0 and 0.5. Their average number is 5–6, while at f > 0.6 and times longer than 4000000 DPD steps they completely coalesce into one cluster (see Fig. 4). Examples of the final states of the simulated system are given in Fig. 5. As before, the core of each cluster is formed by Ag particles, while O and N particles are localized in the cluster shell (see Fig. 5). Control calculations with the doubled number of the DPD steps for f = 0 and 0.5 have not revealed a significant change in the number of SM clusters. Note that, at f = 0.5, the number of the clusters is less than that in the case of f = 0. During the further simulation, the values of СSM and f were varied from 1.5 to 3 vol % and from 0 to 1, respectively. Maximum calculation time tmax was fixed to be 4000000 DPD steps. To monitor the structural
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N
1 2 3 4 5 6
8
4
0 0.5
1.0
1.5
2.0 t, 10 Δt 6
Fig. 4. Number N of clusters composed of SM particles in the simulation cell as a function of simulation time at different parameters СSM and f and Δt ≈ 1.3 ps: СSM = (1−3) 2.0 and (4–6) 2.5 vol %; f = (1, 4) 0.5, (2, 5) 0.6, and (3, 6) 0.75.
transformations in the system, we calculated static structural factor S(q) (Fig. 6) for Ag particles. It was calculated as the average value of the Fourier transform of local density ρ(r) values of the instantaneous states of the system:
S (q) =
∫ dr exp ( −iq ⋅ r )ρ(r) ;
(6)
here, r and q are radius vectors of a point in the real space and in the reciprocal (Fourier) space. Factor S(q) is proportional to the interference part of the radiation intensity scattered on the substance [40]. By definition, limq→0{S(q)} ~ ρκTkBT; therefore, amplitude S(0) is proportional to isothermal compressibility κT, which is related to the density fluctuations in the system. The following relation between the q values corresponding to the reflections in the S(q) plot and real scales is fulfilled: l = 2π/q. In addition, we calculated root-mean-square shift [r( t ) − r(0)]2 for Ag particles, which composed the cores of SM clusters. In the limiting case t → ∞ (when the regime of “normal” diffusion is reached), this characteristic is proportional to diffusion coefficient D 2 [42]: [r( t ) − r(0)] 6t ≈ D. Figure 6 shows structural factors S(q) calculated for systems with СSM = 2.5 vol % and different f values. Their pattern indicates the absence of a long-range order in the system. The profile of S(q) is adequately approximated by the S(0)F(q,R)2 function, where F(q,R) is the shape factor for homogeneous spherical particles [41] with radius R, with this factor being calculated by the following equation: F(q,R) = 3[sin(qR) – qRcos(qR)]/(qR)3,
(7)
which is used when interpreting small-angle neutronscattering data. Since F2(0,R) = 1, this function is multiplied by S(0). Figure 7 exemplifies the approximation of S(q) using F(q,R = 3σ) in the case of f = 0.56 and СSM = 2.5 vol %. Thus, the high degree of similarity of S(q) profiles at different f values is explained by the presence of almost spherical SM clusters (with different diameters) in the simulation cell. In the range of f > 0.6 (see Fig. 8), S(0) dramatically increases, thereby indicating the tendency toward macrophase separation in the system. Indeed, as f increases, all SM clusters in the simulation cell coalesce into one aggregate. Therefore, the S(0) value is stabilized upon a further increase in the salt concentration. In the range of f < 0.6, the value of S(0) also remains almost unchanged, because the number of SM clusters is constant. In this case, the obtained final states were classified on the basis of the calculated diffusion coefficients (Fig. 9). The systems with f < 0.5, in which the diffusion velocity of SM clusters was highest, were interpreted as stabilized colloidal dispersions. The behavior of the system is most interesting in the range 0.55 < f < 0.6, where the diffusion velocity of the clusters is comparable with the diffusion velocity of a single cluster in the case of macrophase separation, when f > 0.65 (Fig. 9). This is related to the fact that SM clusters form metastable aggregates, the morphology of which is gradually transformed and may acquire a fiberlike structure, which is confirmed by the visual inspection of snapshots taken from the simulation cell (see Fig. 10а). The doubling of tmax to 8000000 DPD steps, which was performed for three statistically independent systems, has revealed no COLLOID JOURNAL
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O
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Fig. 5. Snapshots of the state of the system with CSM = 2 vol % after 4000000 DPD steps of simulation corresponding to ≈5.2 μs: f = (a) 0, (b) 0.5, and (c) 1. Water particles have been removed from the simulation cell in order to facilitate visualization. The section of the SM cluster structure is given outside of the simulation cell.
change in the number of the clusters in the system. The morphology of the aggregates is most evident in Fig. 10b illustrating a snapshot for the system with L = 64σ (tmax = 4000000 DPD steps), which has been specially constructed to examine the behavior of the system upon an increase in the sizes of the simulation cell. Thus, the data obtained on the drastic deceleration of the diffusion of SM clusters and their unchanged number, together with the conclusions drawn in [42], lead us to consider the range of f ∈ [0.55, 0.6] to be corresponding to the transition of the system to the gel-like state. COLLOID JOURNAL
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The comparison between the results presented in Figs. 6 and 8–10, enables us to propose the classification of the obtained states of the model CSS and construct the state diagram in the CSM−f coordinates (Fig. 11). The existence of the narrow range of salt concentrations, in which the gel-like state arises, is in qualitative agreement with the experimental data [9– 11]. In the case of СSM ≤ 1.5 vol %, the simulation cell contains a number of SM molecules insufficient for unambiguous interpretation of the final state of the system. For this purpose, calculations should be per-
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S(q)
S(q)
(a)
1
1
0.1
0.1
0.01
0.01
0.1 S(q)
q/2π, 1/σ
(c)
0.1 S(q)
1
1
0.1
0.1
0.01
0.01
0.1
(b)
q/2π, 1/σ
(d)
q/2π, 1/σ
0.1
q/2π, 1/σ
Fig. 6. Structural factors S(q) calculated for Ag particles in the efficient region of the trajectory t > tmax. Parameter f is equal to (a) 0.48, (b) 0.56, (c) 0.7, and (d) 0.75. The volume fraction of SM molecules is СSM = 2.5 vol %.
S(q) S(0) 1.2
2 0.1
1 1.0 0.8
0.01
0.6 1E-3 0.1
q/2π, 1/σ
Fig. 7. (1) Structural factor S(q) calculated for Ag particles at f = 0.56 and СSM = 2.5 vol % and (2) its approximation by the S(0)F(q,R)2 function, where F(q,R) is the shape factor for spherical particles with R = 3σ.
0.4 0.5
0.6
0.7
0.8 f
Fig. 8. The S(0) value as a function of f at СSM = 2.5 vol %. COLLOID JOURNAL
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〈(r(t) – r(0))2〉, σ2
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(a)
800 700 600 500 400 300 1 2 3 4 5
200
100 100
1000
t, 103Δt
Fig. 9. Root-mean-square shift of particles composing SM as a function of simulation time and f at Δt ≈ 1.3 ps. The values of f correspond to the following diffusion coefficients of SM clusters calculated in the range t > 3 × 10 6Δt: D = (1) (2.0 ± 0.40) × 10–12 (f = 0), (2) (1.14 ± 0.09) × 10–12 (f = 0.5), (3) (0.79 ± 0.03) × 10–12 (f = 0.55), (4) (0.73 ± 0.10) × 10–12 (f = 0.6), and (5) (0.80 ± 0.04) × 10–12 m2/s (f = 0.8).
(b)
formed in larger cells, but they are beyond the scope of this study. CONCLUSIONS In this work, we have employed computer simulation based on a coarse-grained model to analyze the role of an electrolyte in the mechanism of the formation of CSS-based hydrogels. The method proposed for the assessment of the role of an incorporated initiating salt by differentiating the interaction of amino and carboxyl groups (coordinated and uncoordinated by a metal ion) with a solvent has enabled us to assert that a gel network is formed in a CSS due to the partial coordination of SM zwitterions with metal ions rather than the weakening of the electrostatic stabilization of SM clusters (because the concentration of the electrolyte is very low and insufficient for gelation). This decreases the solubility of SM clusters (due to the distortion of the network of hydrogen bonds) and promotes their self-assembly. During this process (as has been shown in [15, 16]), SM clusters act as supramonomers, which are further retained due to the hydrogen bonding between uncoordinated amino and carboxyl groups. A previously considered approach to allowance for the presence of the salt [20] supplements the conclusions of this work that gelation in CSS occurs due to the decrease in the solubility of SM clusters. It should be emphasized that we have clearly shown that the main reason for the decrease in the solubility of supramonomers is the complexation of SM with metal ions. COLLOID JOURNAL
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Fig. 10. Snapshots of simulation cells after 4 × 10 6 DPD steps (≈5.2 μs) for CSM = 2.5 vol %: (а) f = 0.55, L = 32σ (the cell is magnified by two times along the x, у, and z axes) and (b) f = 0.55, L = 64σ. The colored scheme for CSS corresponds to Fig. 5; for visualization, all mesoscopic water particles have been removed from cells, while SM clusters have been incorporated into the Connolly surface.
ACKNOWLEDGMENTS We are grateful to the Joint Supercomputer Center of the Russian Academy of Sciences for providing the computational resources of the MVS-100k cluster, as well as to Dr. of Chemistry V.G. Alekseev, Cand. of Physics and Mathematics L.V. Zherenkova (Tver State University), and Dr. of Physics and Mathematics
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f CSM, vol %
0.1 … 0.5
0.55 … 0.6
0.65 … 1
II
III
3 2.5
I
2 1.5
IV
Fig. 11. State diagram plotted for CSS on the basis of the final states of simulation cells. Roman symbols in the scheme correspond to (I) stabilized CSS (SM clusters do not form stable aggregates), (II) gel-like state (metastable aggregates of SM clusters are formed in the system), (III) macrophase separation, and (IV) heavily diluted solution. Total simulation time is tmax = 4000000 DPD steps (≈5.2 μs). For the control, the systems in range II at CSM = 2 vol % were simulated to tmax = 8000000 DPD steps (≈10.4 μs).
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Translated by A. Muravev
