# Time Estimation of Polymer Translocation through Nano-Membrane

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

_{p}= 330 μs. Thus, the results obtained with the described formula are in good agreement with those announced in the specialized literature.

## 1. Introduction

_{x}) and silicon oxide (SiO

_{2}) membranes. These two approaches demonstrate great repeatability and have been widely used in fabricating nanopores, but the method of choice is to drill them using an electron beam in a TEM. Scanning electron microscopy (SEM) is another technique where only milligram quantities of material may be used to determine particle size, shape, and texture [3]. In SEM, a fine beam of electrons scans across the prepared sample in a series of parallel tracks. The electrons interact with the sample and produce several different signals, which can be detected and displayed on the screen of a cathode ray tube. Particles less than 1 nm can be viewed, and since the depth of focus is so much greater than that of the light microscope, information on surface texture can be generated [4].

## 2. Theoretical Background

_{n}, will be the following:

_{1}− μ

_{2}is the chemical potential difference on monomer, between the trans and cis region [16].

_{n}, in the case of polymeric suite by n monomers found in a demi-unbounded domain, into an interaction with a strong barrier and a certain head always fixed at the center of barrier, can be written as follows:

_{n}is equal with ${n}^{\gamma -1}$ that is in Equation (3), the associated free energy becomes the following:

_{m}admits a maximum at the point where derivative I is annulled, as a function of m. The calculations are presented in detail as follows:

_{m}(free energy) function of m, the segments number located in the region on the right, after the barrier, for the two distinct values taken by N (200 and 500) is represented. There are two curves, having two different colors, depending on the maximum value of N. Thus, we have the orange color for N = 200 and the blue color for N = 500.

#### Average Time of Polymer Translocation

_{m}= F(m), we have the explicit integrals for F(m

_{1}) and F(m

_{2}), as follows:

_{0}is a proportionality constant.

## 3. Materials and Methods

#### The Polymer Escape Probability

_{e}, evidently function of escape time t

_{e}, for time-drive established at 200 μs, is represented in Figure 5 [21]. Every diagrammatic item of data has been estimated from about 1000 cases fulfilled, as pictured in histograms form out of the graphical representation, according to Figure 6.

_{e}, is determined at every passage and the histogram of transport escape length period has been realized out of 5000 passages (principal image of presentation), Figure 6. The longest-lasting likely escape time (top of present histogram repartition) is indicated to be t

_{e}= 285 μs.

## 4. Results Discussions

_{64}and (b) poly (dA

_{64}dC

_{64}), respectively.

_{1}= μ

_{2}, are the following:

^{2}, the red color represents the variation as a function of N

^{3}, and the green color represents variation as a function of exp (N).

_{p}, with N has been experimentally verified for DNA molecules larger than 12 nucleotides [26,27].

## 5. Conclusions

_{e}, has been determined at every polymer transition, and the long time period histogram of individual processes has been realized out of 5000 passages. The longest-lasting likely escape time (noted at the top of the present histogram repartition) is determined to be t

_{p}= 330 μs.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Polymer escape in transition, having m monomers in the trans area. I is the cis area, while II is the trans area.

**Figure 3.**Associated free energy barrier F

_{m}for m segments located in trans region. The maximum of the function is the value of the function for m = m* and is denoted by F* = F(m*).

**Figure 7.**Translocation times histogram: (

**a**) poly(dAdC)

_{64}and (

**b**) poly(dA

_{64}dC

_{64}) under F = 0.5 [13].

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**MDPI and ACS Style**

Paun, M.-A.; Paun, V.-A.; Paun, V.-P.
Time Estimation of Polymer Translocation through Nano-Membrane. *Polymers* **2022**, *14*, 2090.
https://doi.org/10.3390/polym14102090

**AMA Style**

Paun M-A, Paun V-A, Paun V-P.
Time Estimation of Polymer Translocation through Nano-Membrane. *Polymers*. 2022; 14(10):2090.
https://doi.org/10.3390/polym14102090

**Chicago/Turabian Style**

Paun, Maria-Alexandra, Vladimir-Alexandru Paun, and Viorel-Puiu Paun.
2022. "Time Estimation of Polymer Translocation through Nano-Membrane" *Polymers* 14, no. 10: 2090.
https://doi.org/10.3390/polym14102090