=====
Units
=====

.. role:: raw-latex(raw)
   :format: latex
..

.. raw:: latex

   \maketitle

Notation
--------

| We use the following definitions:

+---------------+--------------+-----------------------------------+
| Command       | ``double``   | ``string``                        |
+===============+==============+===================================+
| ``hunits``    | :math:`l`    | **l_unit**                        |
+---------------+--------------+-----------------------------------+
| ``temp``      | :math:`T`    | **T_unit**                        |
+---------------+--------------+-----------------------------------+
| ``mass``      | :math:`m`    | **m_unit**                        |
+---------------+--------------+-----------------------------------+
| ``viscosity`` | :math:`\eta` | :math:`\mathbf{\eta}`\ **\_unit** |
+---------------+--------------+-----------------------------------+

Properties with length scaling
------------------------------

If the units of the output is length to the :math:`x` power, and
:math:`r` is the result prior to unit conversion, then the output is

:math:`r \cdot l^x` **l_unit**\ :math:`^x`.

.. _intrinsic-viscosity-with-mass-units-1:

Intrinsic viscosity with mass units
-----------------------------------

If **l_unit** = ``L``, then

:math:`[\eta]_{m}=q_\eta \langle\alpha\rangle/m \cdot l^3`
**l_unit**\ :math:`^3`/**m_unit**

else

:math:`[\eta]_{m}=q_\eta \langle\alpha\rangle/m \cdot l^3 a_{l}^3 a_{m}`
``cm``\ :math:`^3`/``g``.

.. _friction-coefficient-1:

Friction coefficient
--------------------

| If **l_unit** is different than ``L``, then

:math:`f = 6\pi\eta R_H \cdot 10^{-2} l a_l a_\eta`
``dyne``\ :math:`\cdot`\ ``s``/``cm``.

.. _diffusion-coefficient-1:

Diffusion coefficient
---------------------

| If **l_unit** is different than ``L``, then

:math:`D = k_{B}(T + a_T)/(6\pi\eta R_H) \cdot 10^{9} l^{-1} a_l^{-1} a_\eta^{-1}`
``cm``\ :math:`^2`/``s``.

.. _sedimentation-coefficient-1:

Sedimentation coefficient
-------------------------

| If **l_unit** is different than ``L``, then

:math:`s = mb/(6\pi\eta R_H) \cdot 10^{15} l^{-1} a_l^{-1} a_\eta^{-1} a_m^{-1}`
``Sved``.

Conversion tables
-----------------

+------------+-----------------+-------------+
| **l_unit** | :math:`a_{l}`   | uncertainty |
+============+=================+=============+
| ``m``      | 100             | 0           |
+------------+-----------------+-------------+
| ``cm``     | 1               | 0           |
+------------+-----------------+-------------+
| ``nm``     | :math:`10^{-7}` | 0           |
+------------+-----------------+-------------+
| ``A``      | :math:`10^{-8}` | 0           |
+------------+-----------------+-------------+

| 

+------------+---------------+-------------+
| **T_unit** | :math:`a_{T}` | uncertainty |
+============+===============+=============+
| ``C``      | 273.15        | 0           |
+------------+---------------+-------------+
| ``K``      | 0             | 0           |
+------------+---------------+-------------+

| 

+------------+-------------------------------+-----------------+
| **m_unit** | :math:`a_{m}`                 | uncertainty     |
+============+===============================+=================+
| ``Da``     | :math:`6.02214 \cdot 10^{23}` | :math:`10^{18}` |
+------------+-------------------------------+-----------------+
| ``kDa``    | :math:`6.02214 \cdot 10^{20}` | :math:`10^{15}` |
+------------+-------------------------------+-----------------+
| ``g``      | :math:`1`                     | 0               |
+------------+-------------------------------+-----------------+
| ``kg``     | :math:`10^{-3}`               | 0               |
+------------+-------------------------------+-----------------+

| 

+--------------------------+------------------+-------------+
| :math:`\eta`\ **\_unit** | :math:`a_{\eta}` | uncertainty |
+==========================+==================+=============+
| ``cP``                   | 1                | 0           |
+--------------------------+------------------+-------------+
| ``P``                    | 100              | 0           |
+--------------------------+------------------+-------------+

| 

+--------------------------------+------------------+
| :math:`k_B`                    | uncertainty      |
+================================+==================+
| :math:`1.38065 \cdot 10^{-23}` | :math:`10^{-28}` |
+--------------------------------+------------------+