Units¶
Notation¶
We use the following definitions:
| Command | double |
string |
|---|---|---|
hunits |
\(l\) | l_unit |
temp |
\(T\) | T_unit |
mass |
\(m\) | m_unit |
viscosity |
\(\eta\) | \(\mathbf{\eta}\)_unit |
Properties with length scaling¶
If the units of the output is length to the \(x\) power, and \(r\) is the result prior to unit conversion, then the output is
\(r \cdot l^x\) l_unit\(^x\).
Intrinsic viscosity with mass units¶
If l_unit = L, then
\([\eta]_{m}=q_\eta \langle\alpha\rangle/m \cdot l^3\) l_unit\(^3\)/m_unit
else
\([\eta]_{m}=q_\eta \langle\alpha\rangle/m \cdot l^3 a_{l}^3 a_{m}\)
cm\(^3\)/g.
Friction coefficient¶
If l_unit is different than
L, then\(f = 6\pi\eta R_H \cdot 10^{-2} l a_l a_\eta\)
dyne\(\cdot\)s/cm.
Diffusion coefficient¶
If l_unit is different than
L, then\(D = k_{B}(T + a_T)/(6\pi\eta R_H) \cdot 10^{9} l^{-1} a_l^{-1} a_\eta^{-1}\)
cm\(^2\)/s.
Sedimentation coefficient¶
If l_unit is different than
L, then\(s = mb/(6\pi\eta R_H) \cdot 10^{15} l^{-1} a_l^{-1} a_\eta^{-1} a_m^{-1}\)
Sved.
Conversion tables¶
| l_unit | \(a_{l}\) | uncertainty |
|---|---|---|
m |
100 | 0 |
cm |
1 | 0 |
nm |
\(10^{-7}\) | 0 |
A |
\(10^{-8}\) | 0 |
| T_unit | \(a_{T}\) | uncertainty |
|---|---|---|
C |
273.15 | 0 |
K |
0 | 0 |
| m_unit | \(a_{m}\) | uncertainty |
|---|---|---|
Da |
\(6.02214 \cdot 10^{23}\) | \(10^{18}\) |
kDa |
\(6.02214 \cdot 10^{20}\) | \(10^{15}\) |
g |
\(1\) | 0 |
kg |
\(10^{-3}\) | 0 |
| \(\eta\)_unit | \(a_{\eta}\) | uncertainty |
|---|---|---|
cP |
1 | 0 |
P |
100 | 0 |
| \(k_B\) | uncertainty |
|---|---|
| \(1.38065 \cdot 10^{-23}\) | \(10^{-28}\) |