CN112652364A - Method for predicting critical micelle concentration of surfactant based on de novo calculation model - Google Patents
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- 239000000693 micelle Substances 0.000 title claims abstract description 44
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- 238000004364 calculation method Methods 0.000 title claims abstract description 16
- 239000000126 substance Substances 0.000 claims abstract description 27
- 238000000329 molecular dynamics simulation Methods 0.000 claims abstract description 18
- 239000000178 monomer Substances 0.000 claims abstract description 18
- 229920000642 polymer Polymers 0.000 claims abstract description 9
- 239000002245 particle Substances 0.000 claims description 10
- 238000004088 simulation Methods 0.000 claims description 10
- 230000008859 change Effects 0.000 claims description 8
- 230000010354 integration Effects 0.000 claims description 7
- 238000005094 computer simulation Methods 0.000 claims description 4
- 230000008878 coupling Effects 0.000 claims description 4
- 238000010168 coupling process Methods 0.000 claims description 4
- 238000005859 coupling reaction Methods 0.000 claims description 4
- 238000013459 approach Methods 0.000 claims description 3
- 238000005070 sampling Methods 0.000 claims description 3
- 238000012935 Averaging Methods 0.000 claims description 2
- 238000005411 Van der Waals force Methods 0.000 claims description 2
- 230000002776 aggregation Effects 0.000 claims description 2
- 238000004220 aggregation Methods 0.000 claims description 2
- 239000012298 atmosphere Substances 0.000 claims description 2
- 238000012937 correction Methods 0.000 claims description 2
- 230000003993 interaction Effects 0.000 claims description 2
- 239000000539 dimer Substances 0.000 description 3
- 230000015572 biosynthetic process Effects 0.000 description 2
- 239000002563 ionic surfactant Substances 0.000 description 2
- 238000006116 polymerization reaction Methods 0.000 description 2
- XLYOFNOQVPJJNP-UHFFFAOYSA-N water Substances O XLYOFNOQVPJJNP-UHFFFAOYSA-N 0.000 description 2
- 238000000342 Monte Carlo simulation Methods 0.000 description 1
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- 238000004458 analytical method Methods 0.000 description 1
- 238000000149 argon plasma sintering Methods 0.000 description 1
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- 238000006243 chemical reaction Methods 0.000 description 1
- 239000011362 coarse particle Substances 0.000 description 1
- 239000000084 colloidal system Substances 0.000 description 1
- 238000009792 diffusion process Methods 0.000 description 1
- 238000002474 experimental method Methods 0.000 description 1
- 230000002209 hydrophobic effect Effects 0.000 description 1
- 230000009878 intermolecular interaction Effects 0.000 description 1
- 239000000463 material Substances 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 239000002736 nonionic surfactant Substances 0.000 description 1
- 230000008569 process Effects 0.000 description 1
- 238000011160 research Methods 0.000 description 1
- 239000002904 solvent Substances 0.000 description 1
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Abstract
The invention discloses a method for predicting the critical micelle concentration of a surfactant based on a de novo calculation model, which comprises the following steps: a recursive model is obtained from statistical thermodynamics of chemical positions:
(ii) a And (3) after the occupied volume and the chemical positions of the micelles with different sizes are obtained through molecular dynamics simulation calculation, expressing the concentration of the (n +1) polymer into an analytic function of the concentrations of the monomers and the n polymer by adopting the recursive model. If the monomer concentration is used
As a starting point, the recursive equation can be used to calculate the concentrations of n-mers of different sizes, n =2,3. The method provided by the invention can be applied to various methodsA surfactant of the type.
Description
Technical Field
The invention belongs to the technical field of surfactants, and particularly relates to a method for predicting the critical micelle concentration of a surfactant based on a de novo calculation model.
Background
Surfactants are a class of functional molecules consisting of hydrophobic and hydrophilic groups that are widely used in consumer products, material synthesis, catalytic processes, and chemical industries. The Critical Micelle Concentration (CMC), one of the most important properties of a surfactant, determines the concentration distribution of the surfactant in solution and at the surface, thereby greatly affecting the performance of the surfactant. The calculation and prediction of the critical micelle concentration of the surfactant molecules through a first-order principle can screen the molecules more efficiently with smaller cost. In addition, computational simulations can elucidate microscopic details of polymerization-related structural and energy changes that are difficult to describe experimentally, and this information has high utility for designing new molecules or for modifying known surfactant molecules.
The change of the relevant properties of the surfactant solution with the concentration of the surfactant molecules is detected experimentally by means of conductivity, surface tension, light scattering spectrum and the like. Computational modeling can also simulate the change of surfactant solution systems with solution concentration by molecular dynamics or monte carlo. The magnitude of the critical micelle concentration can be determined by mutating the properties tested near the critical micelle concentration. From a theoretical point of view, CMC can also be predicted by a single-chain mean field (SCMF) method.
Molecular Dynamics (MD) simulations have been used for CMC prediction for certain specific surfactant molecules. However, direct prediction is often difficult for most surfactant molecules due to limitations in the time and spatial dimensions of the simulation system. Typically the surfactant molecules have a CMC of 10-3To 10-6Between mol/L. If a surfactant solution with a concentration around CMC is to be simulated, the number of water molecules required to place 1000 surfactant molecules in the simulation box to form a sufficient number of aggregates is about 5.5X 108And the size of the simulation system must reach at least 255X 255nm3. In addition, micelle formation is controlled by slow diffusion and polymerization kinetics, requiring at least millisecondsOther simulations can yield sufficient statistical samples. However, the cost of implementing this spatial and temporal scale of molecular dynamics simulation at the current computer hardware level is quite expensive. In order to solve the problem of limitation of simulation scale, different research teams develop a plurality of different technical strategies based on a Monte Carlo method, a coarse particle force field, dissipative particle dynamics, an implicit solvent model and an enhanced sampling method. However, this problem is not completely solved and most of the predictive work is still limited to ionic surfactants with relatively high CMC.
The theoretical method can overcome the problems of space and time scale of simulation. For example, Single Chain Mean Field (SCMF) theory, which considers molecular conformation and intermolecular interactions, has been gradually developed as a method for predicting CMC, but these basic models are prone to large deviations when used for prediction of actual surfactant systems due to their approximation and simplification of the models themselves.
Disclosure of Invention
The present invention is directed to a method for predicting the critical micelle concentration of a surfactant based on a de novo model to solve the problems set forth in the background art.
In order to achieve the purpose, the invention provides the following technical scheme:
a method for predicting surfactant critical micelle concentration based on a de novo computational model, comprising the steps of:
the statistical thermodynamic expression of chemical positions is first decomposed into ideal and excess two-part contributions:
wherein k isBIs the boltzmann constant, Λ is the de broglie wavelength of the particle, V and N are the volume and number of particles of the system, respectively, ZN+1And ZNThe configuration integrals of (N +1) particles and N particle systems respectively;
combining step growth models, i.e., assuming that an (n +1) mer is generated by combining an n-mer with a monomer, in equilibrium, the following relationships apply:
μn+1-μn-μ1＝0
a recursive model is obtained:
the physical quantities calculated by molecular dynamics simulation are each V(n)And excess chemical potential in the exponential term; wherein V(n)The calculation method of the occupied volume of the n-polymer is obtained by simple geometric operation according to the assumption that the micelle is in spherical distribution on the whole and by combining the gyration radius size of a single micelle obtained by statistics from a track file of molecular dynamics simulation;
in the recursion model, excess chemical potential on an exponential term is obtained by calculating free energy changes for respectively eliminating one surfactant molecule in a single-molecule solution system and a single micelle solution system by adopting a thermodynamic integration method;
the chemical potential of the single molecule of the surfactant is calculated by adopting an extremely dilute solution model (namely, a surfactant molecule or a single micelle is dissolved in a cubic box system filled with water molecules);
the chemical positions of the monomers in the solution only need to be calculated once, and micelles with the aggregation degrees n being 1,5,10,20,30,40,50,60,80 and 100 are respectively selected as simulation and calculation objects aiming at the chemical positions of the surfactant molecules in micelles with different sizes, and then the chemical positions in all size ranges are obtained through spline interpolation.
Further, the thermodynamic integration method simulates different states of a system by modifying the Hamiltonian quantity:
H(λ)＝H0+λ(H1-H0)
here, H0And H1Respectively, representing the Hamiltonian of the initial state and the final state, and λ is a coupling constant between 0 and 1; the free energy change between the initial and final states is obtained by integration of the coupling constants:
because the interaction between the eliminated molecules and the environment approaches to 0 when lambda is equal to 0, a soft core model (soft core) is adopted to reduce sampling errors; for each system, 19 λ points were selected, namely 0,0.1,0.2,0.3,0.4,0.5,0.55,0.6,0.62,0.65,0.68,0.7,0.72,0.75,0.8,0.85,0.9,0.95, 1.0; in order to improve the calculation accuracy, in the interval with larger free energy, lambda is 0.6-0.75, and more lambda points are added;
for each window, molecular dynamics simulations were performed using a giant canonical ensemble (NPT) at 298K and one atmosphere; the temperature and pressure are controlled by the no é -Hoover method, in which time constants of 100fs and 1000fs, respectively, are used; the cutoff distance for van der waals forces was 1.5nm, containing no long range correction; firstly, performing MD simulation for 10ns to balance the system, and acquiring data in the following 10 ns; in the dense area of the lambda point, the data acquisition time is doubled to reduce errors; standard error sigma of each lambda pointsim(λ) is calculated by a block averaging method, where four blocks of data are used for each point; all molecular dynamics simulations and thermodynamic integral calculations were done using the open source software LAMMPS.
And (3) after the occupied volume and the chemical positions of the micelles with different sizes are obtained through molecular dynamics simulation calculation, expressing the concentration of the (n +1) polymer into an analytic function of the concentrations of the monomers and the n polymer by adopting the recursive model. Then if the monomer concentration is ρ1As a starting point, the recursive equation can be used to calculate the concentrations of n-mers of different sizes, n being 2 and 3, in turn, so as to derive the CMC size.
Compared with the prior art, the invention has the beneficial effects that:
in order to establish a recalculation model and predict CMC and size distribution based on the first principle, the invention provides a novel step growth model based on statistical mechanical definition, which divides chemical potential into ideal part contribution and excess part contribution.
Compared with the previous model based on thermodynamic definition, the models of 1-4 do not need to be calibrated through any empirical parameters. This means that all predictions are based entirely on the calculated data.
The method provided by the invention can be applied to various types of surfactants. For ionic surfactants or mixed surfactants, how to accurately calculate the chemical potential of a single surfactant molecule is a relatively challenging problem. For higher molecular weight surfactants, the shape of the colloid may deviate more from the spherical shape, which may introduce more error to some of the approximation assumptions in the overall prediction model. These are possible shortfalls of this approach and possible further enhancements in the future.
Drawings
FIG. 1 is the calculated excess chemical potential as a function of micelle size in the examples;
FIG. 2a shows the values of C at different surfactant concentrations in the examples12EO12Micelle size distribution in solution systems;
FIG. 2b shows the results of C at different surfactant concentrations in the examples10EO6Micelle size distribution in solution systems.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The following polyethoxy molecules C are used as nonionic surfactants12EO12And C10EO6For example, a CMC prediction flow is illustrated. First, we apply Packmol software to target surfactant moleculesCorresponding unimolecular and single micelle solution models were constructed. For each model, we use the SDK coarse-grained force field to perform MD simulation, and the detailed conditions of the simulation refer to the detailed description in the above summary. Then calculating the free energy change, namely excess chemical potential, of each system for eliminating a single surfactant molecule by a thermodynamic integration method. Figure 2 shows the calculated change in excess chemical potential of individual surfactant molecules in micelles of different sizes. Meanwhile, the gyration radii of the micelles with different sizes can be calculated according to the MD simulated track file, and then the occupied volumes of the micelles with different sizes are estimated (see table 1), and the micelle size data listed in the table can be estimated according to interpolation. According to the calculated chemical potential change condition and the occupied volume of the micelles, the recursive equation deduced in the previous step is combined, and the concentrations of the micelles with different sizes in the solution can be calculated on the premise of giving any monomer concentration. With C10EO6For example, assume a monomer concentration of 10-5mol/L, conversion to obtain monomer particle number density rho1About 6.02X 1021/m3Occupation volume V of monomers and dimers(1)And V(2)Are respectively about 0.9nm3，1.8nm3Excess chemical potential difference of monomer
About 0, the excess chemical potential difference between the dimer micelle and the monomer
About 2.1kJ/mol, and substituting into the recursive model, the dimer concentration is:
the trimer concentration was:
the same can be used to obtain the micelle concentration of other different sizes in turn.
Table 1 analyses the volume occupied by micelles of different sizes estimated from the simulated trajectories.
FIGS. 2a and 2b show the variation of micelle size distribution in solution with monomer concentration, and the CMC size can be predicted based on the assumption of critical state (the critical point is the polymer concentration is greater than the monomer concentration).
TABLE 2 comparison of the predicted CMC values with the results predicted by experimental and other theoretical methods
Table 2 shows the predicted CMC and maximum micelle size distribution and comparison with experimental values and results predicted by other methods. It can be seen that the CMC value predicted by the method has a high degree of coincidence with the experimental value, the deviation is much smaller than the error of the experiment, and the maximum micelle size distribution predicted by the method is more accurate than the prediction results of other theoretical methods.
Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.
Claims (3)
1. A method for predicting the critical micelle concentration of a surfactant based on a de novo model, comprising the steps of:
the statistical thermodynamic expression of chemical positions is first decomposed into ideal and excess two-part contributions:
wherein k isBIs the boltzmann constant, Λ is the de broglie wavelength of the particle, V and N are the volume and number of particles of the system, respectively, ZN+1And ZNThe configuration integrals of (N +1) particles and N particle systems respectively;
combining step growth models, i.e., assuming that an (n +1) mer is generated by combining an n-mer with a monomer, in equilibrium, the following relationships apply:
μn+1-μn-μ1＝0
a recursive model is obtained:
the physical quantities calculated by molecular dynamics simulation are each V(n)And excess chemical potential in the exponential term; wherein V(n)The calculation method of the occupied volume of the n-polymer is obtained by simple geometric operation according to the assumption that the micelle is in spherical distribution on the whole and by combining the gyration radius size of a single micelle obtained by statistics from a track file of molecular dynamics simulation;
and (3) after the occupied volume and the chemical positions of the micelles with different sizes are obtained through molecular dynamics simulation calculation, expressing the concentration of the (n +1) polymer into an analytic function of the concentrations of the monomers and the n polymer by adopting the recursive model. Then if the monomer concentration is ρ1As a starting point, the recursive equation can be used to calculate the concentrations of n-mers of different sizes, n being 2 and 3, in turn, so as to derive the CMC size.
2. The method for predicting the critical micelle concentration of the surfactant based on the de novo calculation model as claimed in claim 1, wherein in the recursive model, the excess chemical potential in the exponential term is obtained by calculating the free energy change for eliminating one surfactant molecule in the single-molecule solution system and the single-micelle solution system respectively by adopting a thermodynamic integration method;
the chemical potential of the single molecule of the surfactant is calculated by adopting an extremely dilute solution model;
the chemical positions of the monomers in the solution only need to be calculated once, and micelles with the aggregation degrees n being 1,5,10,20,30,40,50,60,80 and 100 are respectively selected as simulation and calculation objects aiming at the chemical positions of the surfactant molecules in micelles with different sizes, and then the chemical positions in all size ranges are obtained through spline interpolation.
3. The method for predicting critical micelle concentration of surfactant based on de novo computational model according to claim 2,
the thermodynamic integration method simulates different states of a system by modifying the Hamiltonian quantity:
H(λ)＝H0+λ(H1-H0)
H0and H1Respectively, representing the Hamiltonian of the initial state and the final state, and λ is a coupling constant between 0 and 1; the free energy change between the initial and final states is obtained by integration of the coupling constants:
because the interaction between the eliminated molecules and the environment approaches to 0 when lambda is equal to 0, a soft kernel model is adopted to reduce sampling errors; for each system, 19 λ points were selected, namely 0,0.1,0.2,0.3,0.4,0.5,0.55,0.6,0.62,0.65,0.68,0.7,0.72,0.75,0.8,0.85,0.9,0.95, 1.0; in order to improve the calculation accuracy, in the interval with larger free energy, lambda is 0.6-0.75, and more lambda points are added;
for each window, molecular dynamics simulations were performed at 298K and one atmosphere using a giant canonical ensemble; the temperature and pressure are controlled by the no é -Hoover method, in which time constants of 100fs and 1000fs, respectively, are used; the cutoff distance for van der waals forces was 1.5nm, containing no long range correction; headPerforming MD simulation for 10ns to balance the system, and acquiring data in the following 10 ns; in the dense area of the lambda point, the data acquisition time is doubled to reduce errors; standard error sigma of each lambda pointsim(λ) is calculated by block averaging, where four blocks of data are used for each point.
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN114334009A (en) * | 2021-12-31 | 2022-04-12 | 北京博康健基因科技有限公司 | Dynamic prediction method and device for carbon-terminal amidated polypeptide structure |
| GB2603532A (en) * | 2021-02-09 | 2022-08-10 | Res & Innovation Uk | Estimating properties of surfactant mixtures |
| CN115440319A (en) * | 2022-08-03 | 2022-12-06 | 电子科技大学长三角研究院(湖州) | Novel method for simulating amorphization of material structure |
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| FI20065774A0 (en) * | 2006-12-05 | 2006-12-05 | Paavo Kinnunen | Procedure for predicting the properties of a substance that causes phospholipidosis |
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| GB2603532A (en) * | 2021-02-09 | 2022-08-10 | Res & Innovation Uk | Estimating properties of surfactant mixtures |
| CN114334009A (en) * | 2021-12-31 | 2022-04-12 | 北京博康健基因科技有限公司 | Dynamic prediction method and device for carbon-terminal amidated polypeptide structure |
| CN115440319A (en) * | 2022-08-03 | 2022-12-06 | 电子科技大学长三角研究院(湖州) | Novel method for simulating amorphization of material structure |
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