# Attractive and repulsive colloid under shear

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### Owners (the only ones with the permission to edit the main text)

Saheli, Giuseppe

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## Background

>Systems with very short range attractive potential shows a reentrance in the phase space. For example,[reference](https://www.nature.com/articles/nmat752) for particles interacting via square well potential with very short attraction range ($\leq0.03$ particle diameters), it has been observed that at a range of certain high packing fraction, the diffusivity of the system at very low and at high temperature is lower compared to its diffusivity in intermediate temperatues. At low temperatures, the square well plays a role to create attractive bonds and thus giving attractive colloids. But at high temperature, energy of the system is high enough to overlook the attractive well but structural cages due to repulsion of core results in repulsive glass. We are interested to see the behaviour of them under shear deformation.

## Plans
...

## To Do
:::success
green is for finished tasks
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### Equilibrium
:::success
* Implementing the smoothing at the cut-off and verify that the properties you have calculated so far are not different. Everything should be done again for the smoothed version of the potential to avoid any confusion. This means that you will have to produce new confs for T=0.27 and T=0.45 with the smoothing.

* Find a temperature between $T=1.5$ and $T=2.0$ where the the diffusivity is as closed as possible to $T=0.27$. In this way we will have an *Attractive* glass (AG) and *Repulsive* glass (RG) with same diffusivity.
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* Do the search for $N=4000$ and verify that it is ok also for $N=32k$ and $N=64k$
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* Extract $\tau_\alpha(q)$ for the AA and BB from the time at which the correlators have droped to 0.1. Make a graph to compare AG an RG.

### IS
* For the same initial configuration, Calculate IS with and without smooting using both CG, FIRE and Lineforce zero. Discuss the results.

### AQS
* For N=4000 particles, re do stress strain curves usinig smoothed potential and again CG, FIRE and Lineforce zero. Discuss the results.
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## System
>[name=Saheli]
>To perform MD simulation, we are considering sort range attractive mie potential, of the form,
>$V(r)=c\epsilon[(\frac{\sigma}{r})^{\gamma_{rep}}-(\frac{\sigma}{r})^{\gamma_{att}}]$
Here, $\gamma_{rep}=150$, $\gamma_{att}=140$.

### Dynamics of liquid system

* **Re-entrance: MSD and diffusivity with temperature (Old graphs)**
> [name=Saheli]System size: N=4k. potential Mie/cut, $r_c=2.0$.

| MSD | Diffusivity |
| -------- | -------- |
| |  |

* **Fs(k,t) for three sample temperatures with different diffusivity**
>

| N=4k | N=64k |
|------|-------|
|  |  |

### Implementation of smoothing the potential
> [name=Saheli] We are modifying the potential as follows,
> $V(r)=c\epsilon[(\frac{\sigma}{r})^{\gamma_{rep}}-(\frac{\sigma}{r})^{\gamma_{att}}]+c\epsilon[c_1+c_2(\frac{r}{r_c})^2]$
> I set conditions $V(r_c)=0$ and $F(r_c)=-\frac{dv(r)}{dr}|_{rc}=0$.
> This is the effect of modification for different $r_c$ .
>
>

| $r_c=1.05$ | |
| -------- | -- |
|$r_c=1.1$ | |

> parameter values:
>

| $r_c=1.05$ | $c_1=0.0262945028059$, $c_2=-0.0258774577051$ |
| -------- | -- |
|$r_c=1.1$ |$c1=6.68569711449e-05$, $c_2=-6.58717916378e-05$ |

>[name=Saheli] I choose to work with $r_c=1.1$. I will refer to the smmothed potential as "mie/sf" and without smoothing, "mie/cut". for mie/cut, $r_c=2.0$.

### Diffusivity versus T at $\phi=0.59$
> With mie/cut ($r_c=2.0$) and mie/sf ($r_c=1.1 \sigma_{ij}$) comparing the results.
>

> [name=Saheli] Diffusivity at $T=0.27$ is similar of $T=1.6$.

### $\tau_\alpha(k)$ for smooth potential system:
>[name=Saheli] I computed self intermediate scattering function, $F_s(k,t)$ corresponding to different $k$ values. Then, to get $\tau_\alpha(k)$, I choose a cut off value $F_c=0.3,0.1,0.04$.The time corresponding to this $F_c$ I define as $\tau_\alpha$ and, I determine it by cubic interpolation, since the configurations are stored logarithmically.
>

> Results are for AG (T=0.27) and RG (T=1.6). For A and B types seperately. They are not averaged.

|$F_c=0.3$| $F_c=0.1$ |
|--|--|
|||

|$F_c=0.04$|
|--|
|  |

>**Structure factor at two temperatures**

|$T=0.27$|$T=1.6$|
| --|--|
| | |

>[name=Saheli] For A type, SAA rises at low $k$. I am suspicious why so.

### IS minimization with different algorithms and potential
>[name=Saheli]
>Initial configuration is equilibrated sample at T=0.27.
While minimization, I use min/cut
and mie/sf and for both the cases $r_C=1.1 \sigma_{ij}$

| | cg | fire | cg+forcezero|
| -------- | -------- | -------- |--|
|Stopping criteria| *mie/sf:* ene tol, *mie/cut:* line search alpha zero | *mie/sf:* ene tol, *mie/cut:* ene tol | *mie/sf:* ene tol, *mie/cut:* ene tol |
|$E_{ini}$,$E_{fin}$| *mie/sf:* -2.898,-3.469 *mie/cut:* -2.899, -3.462 |*mie/sf:* -2.898,-3.465 *mie/cut:* -2.899, -3.468 |*mie/sf:* -2.898,-3.467 *mie/cut:* -2.899, -3.469 |
|$F_{ini}$, $F_{fin}$ two norm | *mie/sf:* 10543.3, 9.90078 *mie/cut:* 10543.3, 49.7461 | *mie/sf:* 10543.3, 0.053992 *mie/cut:* 10543.3, 0.0139993 | *mie/sf:* 10543.3, 0.000655 *mie/cut:* 10543.3, 0.001307 |
|$F_{ini}$, $F_{fin}$ max component | *mie/sf:* 593.35, 3.45133 *mie/cut:* 593.357, 19.362 | *mie/sf:* 593.35, 0.032609 *mie/cut:* 593.357, 0.00694 | *mie/sf:* 593.35, 9.163e-05 *mie/cut:* 593.357, 0.00024524 |
|wall time | *mie/sf:* **20 s** *mie/cut:* 07 s | *mie/sf:* **44 s** *mie/cut:* 55 s | *mie/sf:* **06 s** *mie/cut:* 07 s |

### AQS: Under uniform shear deformation
> [name=Saheli] With smooth potential mie/sf and 4000 particles, the system is uniformly shear in one direction in strain steps $d\gamma=0.0001$. The results below are for AG (T=0.27) and RG (T=1.6).

* **Stress versus strain**

|cg | cg+forcezero|
|--|--|
|  |  |

>[name=Saheli] Following T=1.6 (Red curve), The system yields after 0.01. From 0.01 to 0.04 stress increases. 0.04 to 0.1 it is in a steady state. After 0.1, AG and RG are in same state.

* **Energy versus strain**

|cg | cg+forcezero|
|--|--|
|  | |

> [name=Saheli]It seems, the major changes in energy behaviour happens at certain strain values. For example, following T=0.27 (Black curve), upto 0.01 energy decreases. Then it firt increases with a certain slope up to ~0.06. Then, its increases with a different slope upto ~ 0.1. Then it becomes steady.
>

* **Earliar results**
> [name=Saheli] I had results for 64k particles mie/cut, $r_c=2.0$ and minimization via cg+forcezero. Here. AG is $T=0.27$ and RG is $T=1.5$.

|stress|energy|
|--|--|
| |  |

>[name=Saheli] results agree with observations from smooth potential 4k system.
>

### Choice of $d\gamma$:

From same initial configuration, using cg+forcezero, shearing the system. With strain steps $d\gamma=0.0002,0.0001,0.00005,0.00001$. For Kob-Andersen, we used $0.0002$.

|energy|stress|
|--|--|
|  |  |

>[name=Saheli] all the above strain steps follow the same trend.
>

### Uniform shear for larger system size:
>[name=Saheli] For A system size N=32k, uniform shear with $d\gamma=0.0002$ and smooth mie potential, we present energy and stress under shear deformation
>

|energy|stress|
|--|--|
|  | |

> Results are similar to what we observe for smaller size N=4k.

### Cyclic shear deformation

>[name=Saheli] For system size N=4k, we shear attractive and repulsive glass. We present the data for energy .
>

|Energy Vs. Cycles|
|--|
||

> [name=Saheli] Yielding occurse above $\gamma_{max}=0.01$. For large amplitude, they reach the same energy state.