Determining intrinsic viscosity and Huggins constant of an unknown sample
The present disclosure describes a computer implemented method, a system, and a computer program product of determining intrinsic viscosity and Huggins constant of an unknown sample. In an embodiment, the method, system, and computer program product include, receiving specific viscosity values over time from a viscometer corresponding to a series of aliquots of an unknown sample injected into an instrument chain where the instrument chain includes the viscometer, calculating a total mass of each of the aliquots, calculating a first intermediate viscosity value of each of the aliquots, calculating a second intermediate viscosity value of each of the aliquots, and fitting the total mass, the first intermediate viscosity value, and the second intermediate viscosity value to a fitting, resulting in a calculated intrinsic viscosity of the unknown sample and a calculated Huggins constant of the unknown sample.
1 . A computer implemented method comprising:
receiving, by a the computer system from a viscometer integrated into an instrument chain, specific viscosity values over time, η sp (t), from a viscometer,
wherein the specific viscosity values correspond to a series of aliquots of an unknown sample injected into the instrument chain,
executing, by the computer system, a set of logical operations calculating a total mass of each of the aliquots, m i , as a function of a volume of the each of the aliquots, v i , and a concentration of the each of the aliquots, c i ; wherein the total mass of each of the aliquots, mi, is further calculated by numerically integrating concentration detector signal values, cmeas(t), received from a concentration detector over a defined time interval corresponding to each aliquot as a first integral function;
executing, by the computer system, a set of logical operations calculating a first intermediate viscosity value of the each of the aliquots, I η i , as a second integral function of the received specific viscosity values, η sp (t), corresponding to the each of the aliquots;
executing, by the computer system, a set of logical operations calculating a second intermediate viscosity value of the each of the aliquots, I2η i , as a third integral function of the received specific viscosity values, η sp (t), corresponding to the each of the aliquots; and
executing, by the computer system, a set of logical operations fitting the total mass of the each of the aliquots, m i , the first intermediate viscosity value of the each of the aliquots, Iη i , and the second intermediate viscosity value of the each of the aliquots, I2η i , to a fitting function comprising the first integral function, a floating intrinsic viscosity of the unknown sample, [η], the second integral function, a floating Huggins constant of the unknown sample, K h , and the third integral function, resulting in a calculated intrinsic viscosity of the unknown sample and a calculated Huggins constant of the unknown sample, wherein the method is performed by a special-purpose system configured to analyze sensor data from physical laboratory instrumentation and the specific viscosity values are based on time-varying physical measurements.
2 . The method of claim 1 wherein the viscometer is a differential viscometer.
3 . The method of claim 1 wherein the total mass of the each of the aliquots, m i , is
m i =v i c i .
4 . The method of claim 1 wherein the second integral function is
I
η
i
=
∫
peak
,
i
η
sp
(
t
)
dt
.
5 . The method of claim 1 wherein the third integral function is
I
2
η
i
∫
peak
,
i
η
sp
2
(
t
)
dt
.
6 . The method of claim 1 wherein the fitting comprises a least squares fitting.
7 . The method of claim 6 wherein the least squares fitting comprises a non-linear least squares fitting algorithm executed by the computer system to fit the total mass of each of the aliquots, m i , to the fitting function comprising a multi-parameter fitting function comprising the floating intrinsic viscosity of the unknown sample, [η], and the floating Huggins constant of the unknown sample, K h .
8 . The method of claim 1 wherein the fitting function is
m
i
=
1
[
η
]
I
η
i
-
1
[
η
]
I
2
η
i
.
9 . The method of claim 1 further comprising
executing, by the computer system, a set of logical operations calculating a figure of merit, FOM, characterizing a contribution of K h to fitting, as a ratio function of K h , the second intermediate viscosity value of the each of the aliquots, I2η i , and the first intermediate viscosity value of the each of the aliquots, Iη i .
10 . The method of claim 9 wherein the ratio function is
FOM=( K h I 2η i )/ Iη i .
11 . The method of claim 1 further comprising
executing, by the computer system, a set of logical operations calculating a ratio of the first intermediate viscosity value of the each of the aliquots, Iη i , to the total mass of the each of the aliquots, m i ; and
displaying, by the computer system, a plot of the calculated ratio of the each of the aliquots versus the total mass, m i , of the each of the aliquots.
12 . A computer implemented method comprising:
receiving, by a computer system from a viscometer integrated into an instrument chain, specific viscosity values over time, η sp (t), from a viscometer,
wherein the specific viscosity values correspond to a series of aliquots of an unknown sample injected into the instrument chain,
wherein the instrument chain comprises the viscometer,
executing, by the computer system, a set of logical operations calculating a first intermediate viscosity value of the each of the aliquots, Iη i , as a second integral function of the received specific viscosity values, η sp (t), corresponding to the each of the aliquots;
executing, by the computer system, a set of logical operations calculating a second intermediate viscosity value of the each of the aliquots, I2η i , as a third integral function of the received specific viscosity values, η sp (t), corresponding to the each of the aliquots; and
executing, by the computer system, a set of logical operations fitting a total mass of the each of the aliquots, m i , the first intermediate viscosity value of the each of the aliquots, Iη i , and the second intermediate viscosity value of the each of the aliquots, I2η i , to a fitting function comprising the first integral function, a floating intrinsic viscosity of the unknown sample, [η], the second integral function, a floating Huggins constant of the unknown sample, K h , and the third integral function, resulting in a calculated intrinsic viscosity of the unknown sample and a calculated Huggins constant of the unknown sample, wherein the method is performed by a special-purpose system configured to analyze sensor data from physical laboratory instrumentation and the specific viscosity values are based on time-varying physical measurements, and wherein the total mass of each of the aliquots, mi, is further calculated by numerically integrating concentration detector signal values, cmeas(t), received from a concentration detector over a defined time interval corresponding to each aliquot as a first integral function.
13 . The method of claim 12 wherein the viscometer is a differential viscometer.
14 . The method of claim 12 wherein the second integral function is
I
η
i
=
∫
peak
,
i
η
sp
(
t
)
dt
.
15 . The method of claim 12 wherein the third integral function is
I
2
η
i
∫
peak
,
i
η
sp
2
(
t
)
dt
.
16 . The method of claim 12 wherein the fitting comprises a least squares fitting.
17 . The method of claim 16 wherein the least squares fitting comprises a non-linear least squares fitting algorithm executed by the computer system to fit the total mass of each of the aliquots, m i to the fitting function comprising a multi-parameter fitting function comprising the floating intrinsic viscosity of the unknown sample, [η], and the floating Huggins constant of the unknown sample, K h .
18 . The method of claim 12 wherein the fitting function is
m
i
=
1
[
η
]
I
η
i
-
1
[
η
]
I
2
η
i
.
19 . The method of claim 12 further comprising
executing, by the computer system, a set of logical operations calculating a figure of merit, FOM, characterizing a contribution of K h to fitting, as a ratio function of K h , the second intermediate viscosity value of the each of the aliquots, I2η i , and the first intermediate viscosity value of the each of the aliquots, Iη i .
20 . The method of claim 19 wherein the ratio function is
FOM=( K h I 2η i )/ Iη i .
21 . The method of claim 12 further comprising
executing, by the computer system, a set of logical operations calculating a ratio of the first intermediate viscosity value of the each of the aliquots, Iη i , to the total mass of the each of the aliquots, m i ; and
displaying, by the computer system, a plot of the calculated ratio of the each of the aliquots versus the total mass, m i , of the each of the aliquots.