Absolute Helmholtz FE of the nanoconfined phase is determined using structures generated in GCMD simulations as input. Number density of the boundary layers, the central layers, and the entire nanoconfined region, as a function of separation.
Understanding the Nanoconfined Fluid
- MEMS/NEMS Development
- Nanoscale Lubrication
- Biological Application
- Importance in AFM Operation
Specifically, liquid handling and liquid processing devices for biological microanalysis and drug delivery are important branches of the many new applications of MEMS/NEMS. Another application is to try to answer one of the fundamental problems in biological science: the origin of life.
Controversy among Experimentalist
- Introduction to SFA/SFB
- Conflicting Results from SFA Community
- Results of AFM Experiments
- Other Techniques
- Consistency in Nanoconfined Water Behavior
By repeating these experiments using a different surface preparation method that eliminated platinum nanoparticle contamination, Granick and colleagues found several orders of magnitude increases in viscosity depending on the deposition rate7. The lack of increase in the viscosity of water can be well explained using the nanoconfined phase transition theory by Radhakrishnan et al.74.
Simulation Research
Pros and Cons of Simulation
Results from Simple Models
Also relevant is the work of Cui et al.83-86, which provides further evidence supporting a first-order phase transition, and the work of Jabbarzadeh et al.87,88, who argue that the high-friction liquid film is metastable rather than thermodynamically stable state, and thus the transition is second order. In the work of Cui et al.83–86, they first note that the formation of an ordered solid-like structure by nanoconfinement depends on the relative strength of the wall-fluid interaction, which only occurs when the wall-fluid interaction is sufficiently strong .
Evidence from Atomistically Detailed Model
In addition, it is not physically realistic to assume that the mica sheets consist only of simple LJ atoms statically located in face-centered cubic (FCC) lattice sites. Given this, it can be argued that the observed phenomena may be different from what occurs in experiment.
Free Energy
Criteria for Defining a Solid
In their simulations, they used a fully atomistically detailed model for both the liquid (dodecane and cyclohexane95) and the solid (mica93), and demonstrated that confined nanofluids undergo a rapid and dramatic transition to a layered structure and sorted (shown in Figure 2.6). . The Verlet criterion that the magnitude of the structure factor at its first peak is 2.897, the Lindeman criterion that the amplitude of vibration of the atoms is not sufficient to occupy the space of their nearest neighbors98 and the Born criterion that the shear force characteristic of solids is present99.
Pivotal Role of FE in Thermodynamics
FE Determination Methodologies
- Fluid FE Calculation
- Solids FE Calculation
The addition of the excessive chemical potential (μex) and the chemical potential of ideal gas under the same conditions (μid) gives absolute FE. Snapshots of the nanoconfined dodecane with a separation equivalent to five molecular layers (adapted from the work of Cummings et al.94).
Choice of Models and Methodology
Models
Consequently, considering the computational cost in the FE calculation (especially since the method used in this work requires twenty simulations to perform a single FE measurement), the classical 12-6 Lennard-Jones (LJ) potential is used to model. interactions in the nanoconfined system. Mainly in this research the Berthelot-Lorentz Combination rules are applied, except for FE calculations of non-proportional systems in section 5.4.
FE Calculation Methodology
Additionally, it is important to note that all the following works use reduced LJ units, except for the scenarios specifically stated. The essential parts of this dissertation research are the evaluation of existing basic Einstein crystal method algorithms, the development of modified algorithms, the adaptation of these algorithms to FE measurements, and the use of FE as a tool to reveal the nature of nanoconfined fluid behavior.
Basic Algorithm
Introduction
- FE of the Reference (A 0 )
- Evaluation of ∆A 1
- Evaluation of ∆A 2
- Parameters Setting
The FE of the reference state, an Einstein crystal, can be calculated analytically by simplifying and evaluating the partition function. In other words, it is the calculated intermolecular interaction potential energy based on configurations of the reference system.
Validation
Monte Carlo versus Molecular Dynamics
Among the possible factors leading to this difference, the divergence of the target temperature and the achieved temperature in the simulation could be the source. As Butler and colleagues revealed, Tcon fig in canonical MC is always less than Tinput (i.e. the desired temperature) and the discrepancy between the two decreases rapidly as the system grows larger (shown in Figure 3.3), becoming less than 0 .2% for 2000 particles.
Modified Algorithm for Nanoconfined System
- FE Calculation for Nanoconfined System
- Modified Tail Correction
- Introduction
- Effectiveness Test
- Adapted Algorithm Validation
- Definition of Separation
The detailed step-by-step derivation of the modified tail correction is included in Appendix A. Now it is necessary to measure the effectiveness of the modified tail correction in potential calculations.
GPU accelerated calculation
Performance Gains via GPU Computing
Definitions of separation in nano-confined system used in this thesis research. left) The solid wall consists of FCC(111) in nano-confined system. A template performance comparison of CPU and GPU in MD simulations was performed with CPU-based LAMMPS and GPU-based HOOMD.
Thermostat in MD
A modified dynamic using a chain of variables (Nos´e-Hoover chain), i.e. chains of thermostats that increase temperature control/stability, instead of a single thermostat variable in the original Nos´e-Hoover dynamics146 has been introduced and is an option to take full advantage of GPE in future FE calculations. In the following dissertation research, the use of the massive parallel computing power of GPE is limited to performing uncoupled molecular simulations.
Role of Simulation Box Shape
A comparison (top) of the dependence of calculated FEs on box shape and a schematic diagram (bottom) showing the types of simulation box shapes used.
Finite System Size Dependence and Correction
Therefore, a universal finite size correction is needed to correct for the systematic error arising from the use of finite system size in the calculation. This suggests that the use of FSC-asymptotic correction as a universal finite size effect compensation strategy is suitable in FE calculations.
Relative Stability of LJ Crystals
Finite Cutoff Radius Effect
As shown in Figure 4.5, calculated FEs show a strong finite cutoff dependence, and each term in the FE calculation has a remarkably different cutoff radius sensitivity. The results in Figure 4.5 clearly show that the final cutoff effect is largely determined by the choice of cutoff radius in ∆A1 evaluation rather than ∆A2.
Wall-Fluid Interaction
The A/NkBT of the bulk solid and liquid is given by von der Hoef's equation123 and Johnson's equation122 respectively. bottom) FCC(111) solid wall with nano-confined FCC(111) crystal. More importantly, along with the increase of the wall-fluid interaction, FE of the confined structure shows a tendency to converge with the FE profile of the bulk fluid at higher temperatures compared to the FE profile of the corresponding bulk solid ( εwm).
Role of Wall-Wall Separation
Structure of Nanoconfined Phase
The strength of the wall-liquid interaction is 4.0 times that of the liquid-liquid interaction (εwm=4.0εmm) and the sigma for the solid wall and the nanoconfined liquid/phase are the same (σww=σmm) .
Fluid-Wall Particle Size Ratio
FE as a function of fluid–wall particle size ratio at different definitions of the wall–fluid interaction range. - Lorenz's rule of combination; (Central) geometric mean; Fixed wall-fluid interaction range (bottom) at σwm=1.
GCMD
Molecular Dynamics Simulations
The limit value for the interaction between mobile particles is set to 3σ (as suggested in section 4.4), with the XPLOR shift starting at 2.75σ. These simulations also use the Nos´e-Hoover thermostat with time step = 0.005 and XPLOR shift from 4.75σ.
Order-disorder Transition Temperature Analysis
These FE measurements also observe that A/NkBT is lower for smaller pores than larger pores, and thus smaller pores should also be expected to have a higher ODT value than the bulk. However, FE measurements in Section 5.2 are limited to ideal nanoconfined FCC structures and are oversimplified.
Free Energy of Nanoconfined Phase
They found that the pressure of the nanoconfined phase is much higher than the corresponding liquid. As shown in Figure 6.3, peaks and valleys exist in the FE curves of the nanoconfined phase in both the liquid and solid states.
Role of Boundary Layers
However, the number of fluid particles in the central layers continues to increase monotonically with greater wall–wall separation. Top left) number of particles in the selected region within the boundary layer at different separations.
Free Energy of Central Region
The free energy of the central region still shows fluctuations in A/NkBT, where peaks occur for non-ideal separations and valleys for ideal separations. Similarly, increasingεwm to 6, A/NkBT of the central region is lowered, shifting convergence with the equivalent density bulk system to a separation exceeding six layers.
Consistency
Experimental Studies
The attraction in the normal force corresponds to a spontaneous process, while the repulsion corresponds to a non-spontaneous process. This means that if a universal theory is to explain most of the research results to date, it must include the oscillation and provide a clear description of that oscillation in the separation-reducing process.
Cumulative FE Measurements
We therefore introduce several assumptions to estimate the absolute FE of the entire system (indicated in Figure 6.3 Below) and we use a hybrid approach to measure the FE. Among these, the FE change of the entire nanoconfined phase (∆ANC) is defined as the change in the product of absolute FE of the nanoconfined phase (AN) and the number of particles in the nanoconfined phase (N); the definition of the FE change of the whole mass fluid system (∆ABC) is based on the assumption that the mass is not affected by the nano-confined and its FE does not change.
Comparison of Specifications in Experiments
This supports the above-mentioned consistency shared by both experimental and simulation studies, and proves that the absolute FE measurement can describe the characteristic property of nanoconfined fluid behavior. Therefore, in the next section we compare the difference in details between both sides of the debate and use absolute FE determination as a tool to further investigate the nature of nano-confined fluid behavior.
Role of Larger Contact Area
The area ratio is ~6.6; Extrapolating this trend, we would expect that an increase in surface contact area by two orders of magnitude would cause the system to take a factor of 75 more time to reach an equivalently ordered state. Clearly this can be further exacerbated by surface size effects, where systems with larger contact areas simply take much longer to reach equilibrium, which can be further amplified by the significant effects affecting the strength of the wall interaction and the pore separation may have on the absolute free energy of the confined phase.
Role of “Jammed” Atoms
However, as the local density increases due to jammed atoms, the FE of the core layers is greatly increased compared to bulk solids. FE of the central atoms as a function of the density of the nanoconfined phase compared to the FE of the bulk at the same density.
Fluid-Solid Oscillation
Although the wall-to-wall separation occurs between an integer number of ideal layers, we assume that the nanoconfined fluid remains in a liquid-like state, which is different from the current way of understanding the behavior of nanoconfined phases. In contrast to Klein's experiment, the trapping of liquid particles in the nano-confined region, even in a quasi-static mode, is highly possible in Granick's experiment.
Configurations at Various Densities
Separation
FE of the central layers in the nanoconfined system as a function of the total density at different number of layers.
Wall-Fluid Interaction
When the density of the confined phase is not equal to unity (especially at a density greater than unity), the FE of the central layers is not always lower at the strongest wall-fluid interaction strength. However, as the density of the nanoconfined phase increases beyond unity (ρ∗> . 1.0), the FE of the central layers increases significantly under almost all conditions of wall–wall separation strength and wall–fluid interaction.
Boundary Layers
Moreover, a local FE minimum of the central layers occurs around the density of the nanoconfined phase equal to unity (ρ∗=1.0) in all four of these interaction strength scenarios. Absolute Helmholtz FE of the central layers and the densities of the central layers, boundary layers, and the entire nanoconfined phase as a function of the density of the nanoconfined fluid.
Conclusions
The much lower free energy of the nanoconfined region compared to its bulk liquid suggests that the liquid may undergo a liquid-to-solid phase transition as the separation decreases. Using this, we calculated the Helmholtz free energy of the central region alone, accounting for the effects of the strong wall interactions.
Future work
Free Energy of Fluid State
Finally, our studies of the nanoconfined system with different densities further support the idea that "pinched" atoms have the ability to destabilize the nanoconfined solid phase and remove the putative liquid-to-solid transition. To summarize, this thesis research reviewed fundamental issues in solid FE determinations, supported the existence of a nanoconfinement-induced liquid-to-solid phase transition via absolute FE measurements, and introduced a theory that better reveals the nature of nanoconfined. fluid behavior and reconciles the difference between experimental studies.
Oscillatory Properties
Chemical Reactions
It will be interesting to investigate the change in chemical reactions that occur in the nano-confined phase, as the wall-wall separation gradually decreases or increases. In nanoconfined systems, correction of the potential for finite cut-off radius includes contributions from both liquid–liquid interaction potential within the nanoconfined phase, and also liquid–wall interaction potential due to the existence of solid walls.
