d_h_parameters.py

epsilon_0 = 8.85418781762e-12 # C^2 * N^-1 * m^-2
pi = 3.14159265359
n_a = 6.02214129e+23 # mol^-1
e = 1.602176565e-19 # C
k_b = 1.3806488e-23 # J K^-1

t_abs = 298.15 # K
epsilon = 78.54*epsilon_0 # at 298.15 K
rho_0 = 0.99714 # kg * L^-1

# alpha
# [=] mol^(-1/2) (kg/L)^(1/2) (C^2/(C^2*N^-1*m^-2*N*m*K^-1*K)))^(3/2)
# [=] (kg/mol * m^3/L)^(1/2) [=] kg^(1/2) mol^(-1/2) * 1000^(1/2)
alpha_dh =  (2*pi*n_a*(rho_0*1000))**(1/2.0) * \
            (e**2/(4*pi*epsilon*k*t_abs))**(3/2.0) 
# beta
# [=] (C^2/mol kg/L * 1000L/m^3 / (C^2 N^-1 m^-2 * N m K^-1 * K))^(1/2) 
# [=] kg^(1/2) mol^(-1/2) m^-1 * 1000^(1/2)
beta_dh = e*(2*n_a*(rho_0*1000)/(epsilon*k_b*t_abs))**(1/2.0)

# A_c NSRDS-NBS-24
# [=] mol^(1/2) * C^3 /(N m K^-1 K )^(3/2)
a_c =   (2*pi*n_a/1000.0)**(1/2.0)*e**3/(np.log(10.0)*k_b**(3/2.0)) * \
        (1/(t_abs**(3/2.0)*epsilon**(3/2.0)))
ac = (2*3.14159265*6.0225228e+23/1000.0)**(1/2.0)*4.8029820e-10**3/(np.log(10.0)*1.3805418e-16*1e-7**(3/2.0)) * \
        (1/(298.15**(3/2.0)*(78.30)**(3/2.0)))
print 'Mortimer 7.4-10'
print 'alpha_dh = ' + str(alpha_dh) + ' kg^(1/2) mol^(-1/2)'
print 'Mortimer 7.4-6'
print 'beta_dh = ' + str('%1.12e' % beta_dh) + ' kg^(1/2) mol^(-1/2) m^-1'
print '==>>'
print 'A_m = alpha_dh/ln(10) = ' + str(alpha_dh / np.log(10.0)) + ' kg^(1/2) mol^(-1/2)'
print 'A_c = A_m/rho_0^(1/2) = ' + str(alpha_dh / np.log(10.0) / rho_0**(1/2.0)) + ' L^(1/2) mol^(-1/2)'
print ''
print 'NSRDS-NBS-24'
print 'A_c = ' + str(ac) + ' L^(1/2) mol^(-1/2) m^-1'
print 'A_c * (T*epsilon)^(3/2) = ' + \
                str('%1.12e' % (ac * (298.15*78.30)**(3/2.0))) + \
                ' L^(1/2) mol^(-1/2) m^-1'