METHOD FOR DETERMINING THE SIZE DISTRIBUTION OF A MIXTURE OF PARTICLES USING TAYLOR DISPERSION, AND ASSOCIATED SYSTEM

摘要

The method comprises the following steps:
injecting (100) a sample into a capillary;transporting (110) the sample along the capillary in experimental conditions suited to generate a Taylor dispersion phenomenon;generating (120) a signal characteristic of the Taylor dispersion;processing (130) the signal in order to obtain the experimental Taylor signal Ŝ(t); andanalysing (200) the experimental Taylor signal Ŝ(t),;The analysis step consists of seeking an amplitude distribution P(G(c)) that allows the experimental Taylor signal Ŝ(t) to be broken down into a sum of Gaussian functions by implementing a constrained regularization algorithm consisting of minimising a cost function Hα including at least one constraint term associated with a constraint that must observe the amplitude distribution P(G(c)) , whereby the minimization is carried out on an interval of interest of the values of the parameter G(c) that is characteristic of the Gaussian amplitude function P(G(c)).

主权项

1. Method for determining the size distribution of a mixture of molecule or particle species comprising the following steps:
injecting a sample of the mixture to be analyzed inside a capillary in which an eluent is flowing; transporting the sample injected along the capillary from an injection section to a detection section thereof, in experimental conditions suitable to generate a Taylor dispersion phenomenon that is measurable at the level of the detection section; generating, by means of a suitable sensor included in the detection section, a signal characteristic of the Taylor dispersion of the transported sample; processing the detection signal in order to obtain an experimental Taylor signal Ŝ(t); and analyzing the experimental Taylor signal Ŝ(t), wherein the step of analyzing an experimental Taylor signal Ŝ(t) of a sample of the mixture consists of searching an amplitude distribution P(G(c)) that allows the experimental Taylor signal Ŝ(t) to be broken down into a sum of Gaussian functions by means of the equation I:
{circumflex over (S)}(t)≡∫0∞P(G(c))G(c)c/2exp[−(t−t0)2G(c)c]dG(c)  (I) where t is a variable upon which the experimental Taylor signal depends and t0 is a value of the variable t common to the various Gaussian functions and corresponding to the peak of the experimental Taylor signal Ŝ(t); G(c) is a characteristic parameter of a Gaussian amplitude function P(G(c)) and is associated: where c=1, with the diffusion coefficient D of a species according to the relation
G(1)=12D/(Rc2t0) for c=−1, to the hydrodynamic ray Rh of a species according to the relationG(-1)=2kBTπηRc2t0Rh-1; and for c=−1/df=−(1+a)/3, to the molar mass M of a species according to the relationG=2kBTπηRc2t0(10πNa3K)1/3M-(1+a3), where kB is the Boltzmann constant, T is the absolute temperature expressed in Kelvins at which the experiment is conducted, η is the viscosity of the eluent used, Rc is the internal ray of the capillary used, Naα is Avogadro's number, and K and a are Mark Houwink coefficients, by implementing a constrained regularization algorithm consisting of minimizing a cost function Hα including at least one constraint term associated with a constraint that must observe the amplitude distribution P(G(c)) that is the solution of the foregoing equation, whereby the minimization is carried out on an interval of interest of the values of the parameter G(c).