def phase_identification_parameter_phase(d2P_dVdT, V=None, dP_dT=None, dP_dV=None, d2P_dV2=None):
    r'''Uses the Phase Identification Parameter concept developed in [1]_ and 
    [2]_ to determine if a chemical is a solid, liquid, or vapor given the 
    appropriate thermodynamic conditions.

    The criteria for liquid is PIP > 1; for vapor, PIP <= 1.

    For solids, PIP(solid) is defined to be d2P_dVdT. If it is larger than 0, 
    the species is a solid. It is less than 0 for all liquids and gases.

    Parameters
    ----------
    d2P_dVdT : float
        Second derivative of `P` with respect to both `V` and `T`, [Pa*mol/m^3/K]
    V : float, optional
        Molar volume at `T` and `P`, [m^3/mol]
    dP_dT : float, optional
        Derivative of `P` with respect to `T`, [Pa/K]
    dP_dV : float, optional
        Derivative of `P` with respect to `V`, [Pa*mol/m^3]
    d2P_dV2 : float, optionsl
        Second derivative of `P` with respect to `V`, [Pa*mol^2/m^6]

    Returns
    -------
    phase : str
        Either 's', 'l' or 'g'
    
    Notes
    -----
    The criteria for being a solid phase is checked first, which only
    requires d2P_dVdT. All other inputs are optional for this reason.
    However, an exception will be raised if the other inputs become 
    needed to determine if a species is a liquid or a gas.
        
    Examples
    --------
    Calculated for hexane from the PR EOS at 299 K and 1 MPa (liquid):
    
    >>> phase_identification_parameter_phase(-20518995218.2, 0.000130229900874, 
    ... 582169.397484, -3.66431747236e+12, 4.48067893805e+17)
    'l'

    References
    ----------
    .. [1] Venkatarathnam, G., and L. R. Oellrich. "Identification of the Phase
       of a Fluid Using Partial Derivatives of Pressure, Volume, and 
       Temperature without Reference to Saturation Properties: Applications in 
       Phase Equilibria Calculations." Fluid Phase Equilibria 301, no. 2 
       (February 25, 2011): 225-33. doi:10.1016/j.fluid.2010.12.001.
    .. [2] Jayanti, Pranava Chaitanya, and G. Venkatarathnam. "Identification
       of the Phase of a Substance from the Derivatives of Pressure, Volume and
       Temperature, without Prior Knowledge of Saturation Properties: Extension
       to Solid Phase." Fluid Phase Equilibria 425 (October 15, 2016): 269-277.
       doi:10.1016/j.fluid.2016.06.001.
    '''
    if d2P_dVdT > 0:
        return 's'
    else:
        PIP = phase_identification_parameter(V=V, dP_dT=dP_dT, dP_dV=dP_dV, 
                                             d2P_dV2=d2P_dV2, d2P_dVdT=d2P_dVdT)
        return 'l' if PIP > 1 else 'g'
def phase_identification_parameter_phase(d2P_dVdT, V=None, dP_dT=None, dP_dV=None, d2P_dV2=None):
    r'''Uses the Phase Identification Parameter concept developed in [1]_ and 
    [2]_ to determine if a chemical is a solid, liquid, or vapor given the 
    appropriate thermodynamic conditions.

    The criteria for liquid is PIP > 1; for vapor, PIP <= 1.

    For solids, PIP(solid) is defined to be d2P_dVdT. If it is larger than 0, 
    the species is a solid. It is less than 0 for all liquids and gases.

    Parameters
    ----------
    d2P_dVdT : float
        Second derivative of `P` with respect to both `V` and `T`, [Pa*mol/m^3/K]
    V : float, optional
        Molar volume at `T` and `P`, [m^3/mol]
    dP_dT : float, optional
        Derivative of `P` with respect to `T`, [Pa/K]
    dP_dV : float, optional
        Derivative of `P` with respect to `V`, [Pa*mol/m^3]
    d2P_dV2 : float, optionsl
        Second derivative of `P` with respect to `V`, [Pa*mol^2/m^6]

    Returns
    -------
    phase : str
        Either 's', 'l' or 'g'
    
    Notes
    -----
    The criteria for being a solid phase is checked first, which only
    requires d2P_dVdT. All other inputs are optional for this reason.
    However, an exception will be raised if the other inputs become 
    needed to determine if a species is a liquid or a gas.
        
    Examples
    --------
    Calculated for hexane from the PR EOS at 299 K and 1 MPa (liquid):
    
    >>> phase_identification_parameter_phase(-20518995218.2, 0.000130229900874, 
    ... 582169.397484, -3.66431747236e+12, 4.48067893805e+17)
    'l'

    References
    ----------
    .. [1] Venkatarathnam, G., and L. R. Oellrich. "Identification of the Phase
       of a Fluid Using Partial Derivatives of Pressure, Volume, and 
       Temperature without Reference to Saturation Properties: Applications in 
       Phase Equilibria Calculations." Fluid Phase Equilibria 301, no. 2 
       (February 25, 2011): 225-33. doi:10.1016/j.fluid.2010.12.001.
    .. [2] Jayanti, Pranava Chaitanya, and G. Venkatarathnam. "Identification
       of the Phase of a Substance from the Derivatives of Pressure, Volume and
       Temperature, without Prior Knowledge of Saturation Properties: Extension
       to Solid Phase." Fluid Phase Equilibria 425 (October 15, 2016): 269-277.
       doi:10.1016/j.fluid.2016.06.001.
    '''
    if d2P_dVdT > 0:
        return 's'
    else:
        PIP = phase_identification_parameter(V=V, dP_dT=dP_dT, dP_dV=dP_dV, 
                                             d2P_dV2=d2P_dV2, d2P_dVdT=d2P_dVdT)
        return 'l' if PIP > 1 else 'g'
def phase_identification_parameter_phase ( d2P_dVdT , V = None , dP_dT = None , dP_dV = None , d2P_dV2 = None ) : if d2P_dVdT > 0 : return 's' else : PIP = phase_identification_parameter ( V = V , dP_dT = dP_dT , dP_dV = dP_dV , d2P_dV2 = d2P_dV2 , d2P_dVdT = d2P_dVdT ) return 'l' if PIP > 1 else 'g'
r'''Uses the Phase Identification Parameter concept developed in [1]_ and 
    [2]_ to determine if a chemical is a solid, liquid, or vapor given the 
    appropriate thermodynamic conditions.

    The criteria for liquid is PIP > 1; for vapor, PIP <= 1.

    For solids, PIP(solid) is defined to be d2P_dVdT. If it is larger than 0, 
    the species is a solid. It is less than 0 for all liquids and gases.

    Parameters
    ----------
    d2P_dVdT : float
        Second derivative of `P` with respect to both `V` and `T`, [Pa*mol/m^3/K]
    V : float, optional
        Molar volume at `T` and `P`, [m^3/mol]
    dP_dT : float, optional
        Derivative of `P` with respect to `T`, [Pa/K]
    dP_dV : float, optional
        Derivative of `P` with respect to `V`, [Pa*mol/m^3]
    d2P_dV2 : float, optionsl
        Second derivative of `P` with respect to `V`, [Pa*mol^2/m^6]

    Returns
    -------
    phase : str
        Either 's', 'l' or 'g'
    
    Notes
    -----
    The criteria for being a solid phase is checked first, which only
    requires d2P_dVdT. All other inputs are optional for this reason.
    However, an exception will be raised if the other inputs become 
    needed to determine if a species is a liquid or a gas.
        
    Examples
    --------
    Calculated for hexane from the PR EOS at 299 K and 1 MPa (liquid):
    
    >>> phase_identification_parameter_phase(-20518995218.2, 0.000130229900874, 
    ... 582169.397484, -3.66431747236e+12, 4.48067893805e+17)
    'l'

    References
    ----------
    .. [1] Venkatarathnam, G., and L. R. Oellrich. "Identification of the Phase
       of a Fluid Using Partial Derivatives of Pressure, Volume, and 
       Temperature without Reference to Saturation Properties: Applications in 
       Phase Equilibria Calculations." Fluid Phase Equilibria 301, no. 2 
       (February 25, 2011): 225-33. doi:10.1016/j.fluid.2010.12.001.
    .. [2] Jayanti, Pranava Chaitanya, and G. Venkatarathnam. "Identification
       of the Phase of a Substance from the Derivatives of Pressure, Volume and
       Temperature, without Prior Knowledge of Saturation Properties: Extension
       to Solid Phase." Fluid Phase Equilibria 425 (October 15, 2016): 269-277.
       doi:10.1016/j.fluid.2016.06.001.
r Uses the Phase Identification Parameter concept developed in [ 1 ] _ and [ 2 ] _ to determine if a chemical is a solid liquid or vapor given the appropriate thermodynamic conditions .