Chemical surface for control of electroosmosis by an applied...

Details Chemical surface for control of electroosmosis by an applied... Chemical surface for control of electroosmosis by an applied...

2000-08-30

2002-12-03

Warden, Jill (Department: 1743)

Chemistry: electrical and wave energy

Processes and products

Electrophoresis or electro-osmosis processes and electrolyte...

Reexamination Certificate

active

06488831

ABSTRACT:

TECHNICAL FIELD OF THE INVENTION
This invention generally relates to electroosmotic surfaces exposed to buffers, and in particular to capillaries or channels having modified electroosmotic surfaces that are used for electrophoretic transport or separations, which permit the fall control of electroosmosis by an applied external voltage field.
BACKGROUND OF THE INVENTION
Electroosmosis is the flow of liquid that is in contact with a solid, under the influence of an applied electric field, The movement of the fluid typically results from the formation of an electric double layer at the solid/liquid interface, i.e., the separation of charge that exists in a thin layer of the surface and in a thin layer of the fluid adjacent to the surface.
Typically electroosmostic flow is observed in capillary electrophoresis which employs a capillary tube having a silica inner surface and which utilizes one or more buffer fluids. In such a configuration electroosmosis arises from interaction of the electric double layer, which is present on the inner-surface/buffer interface of a silica tube, with the longitudinal voltage gradient, wherein the electroosmotic flow rate (&ngr;
eof
) is defined by the following relationship:
 &ngr;
eof
=&zgr;(&egr;
b
/&eegr;)
E
app
=&mgr;
eof
·E
app
  (1)
where &zgr; is the potential drop across the diffuse layer of the electric double layer (commonly referred to as the &zgr; (zeta)-potential), &egr;
b
is the permittivity of the buffer solution, &eegr; is the viscosity of the buffer solution, &mgr;
eof
electroosmotic mobility, and E
app
is the voltage gradient across the length of the capillary or channel. The external flow control effect is directly related to the &zgr;-potential through the changes in the surface charge density of the channel. The total surface charge density results from the chemical ionization (&sgr;
si
) and the charge induced by the radial voltage field (&sgr;
rv
), as described in Hayes et al., “Electroosmotic Flow Control and Monitoring with an Applied Radial Voltage for Capillary Zone Electrophoresis,”
Anal. Chem.,
64:512-516 (1992), which is incorporated herein by reference. According to the capacity model, the &sgr;
rv
is described by the following equation:
&sgr;
rv
=(&egr;
Q
V
r
/r
i
)(1/ln(
r
o
r
i
)  (2)
where &egr;
Q
is the permittivity of the fused silica capillary, V
r
is the applied radial voltage, r
i
is the inner radius of the capillary, and r
o
is the outer radius of the capillary. For a flat plate capacitor model the relationship is:
&sgr;
rv
=(&egr;
Q
V
r
A
e
)/
d
  (3)
where A
e
is the projected area of the radial electrodes on the channel wall and d is the wall thickness in the flat plate capacitor. The surface charge density is related to the &zgr;-potential by the following equation, as described in Bard, et al.,
Electrochemical Methods Fundamentals and Applications.
Wiley and Sons (New York, 1980); Davies, et al.,
Interfacial Phenomena,
2
nd
Ed., Academic Press (New York, 1963); and Overbeek,
Colloid Science,
Kruyt ed., Vol. I, p. 194 (Elsevier, Amsterdam, 1952), which are incorporated herein by reference:
&zgr;=exp(−&kgr;
x
)
E
app
(&egr;
b
/&eegr;)(2
kT/ze
)·sin
h
−1
[(&sgr;
si
+&sgr;
rv
)/(8
kT&egr;
b
n
0
)
½
]  (4)
where
&kgr;=(2
n
0
z
2
e
2
/&egr;
b
kT
)
½
  (5)
and n
0
is the number concentration, z is the electronic charge, e is the elementary charge, T is the temperature, &kgr; is the inverse Debye length, x is the thickness of the counterion, and k is the Boltzmann constant.
Areas of the capillary, which are not under direct control of the external voltage, are still effected by the radial field by a mechanism attributed to surface conductance effects, as described in Wu, et al., “Leakage current consideration of capillary electrophoresis under electroosmotic control”
J. Chromatogr.,
652:277-281 (1993); Hayes, et al., “Electroosmotic Flow Control and Surface Conductance in Capillary Zone Electrophoresis,”
Anal. Chem.,
65:2010-2013 (1993); and Wu, et al., “Dispersion studies of capillary electrophoresis with direct control of electroosmosis,”
Anal. Chem.,
65:568-571 (1993). The magnitude of this effect may be approximated by a &zgr;-potential averaging approach. The &zgr;-potential in the uncovered zones is the average of the &zgr;-potential in the controlled zones and the &zgr;-potential from charge generated from the fused silica surface chemical equilibrium. The &zgr;-potential for the surface chemical equilibrium may be obtained directly from flow measurements in the capillary without an applied external voltage, as described in Overbeek, at p. 194. The resulting flow (&ngr;
obs
) through the capillary which is generated from these sections according to the following relationship, as described in Hayes et al., at pp.512-516:
 &ngr;
obs
=x′&ngr;
r
+(1−
x
′)&ngr;
av
  (6)
where x′ is the fraction of the capillary under the influence of the applied radial voltage (x′>0), &ngr;
r
is the electroosmotic flow rate if the entire capillary were under radial voltage effects (which may be calculated from equations 1 and 4, with 2 or 3), and &ngr;
av
is the average electroosmotic flow generated from surface charge due to chemical equilibrium and the surface charge in the controlled zone due to radial voltage effects.
The voltage gradient across the capillary also induces an additional movement of charged species according to:
&ngr;
em
=(&mgr;
eof
+&mgr;
em
)·
E
app
  (7)
where &ngr;
em
is the migration rate of a charged species, and &mgr;
em
is the electrophoretic mobility of that charged species. Since &mgr;
em
is constant under these experimental conditions, any change in &ngr;
em
may be attributed to changes in &mgr;
eof
.
To obtain an expression directly relating changes in elution time (&Dgr;t
el
) and the change in surface charge density (&Dgr;&sgr;
t
), it is noted that elution time is t
el
=L/&ngr;
em
, wherein L is the length of the capillary from the injector to the detector and &ngr;
em
is the velocity of the analyte. The velocity of the analyte is described by equation 7 where the electrophoretic mobility of that charged species is a constant under these experimental conditions. Noting that &mgr;
eo
is equal to &zgr;·(&egr;
b
/&eegr;) (see equation 1) and the definition for t
el
, the following expression can be derived:
t
el
=L
/[(&zgr;(&egr;
b
/&eegr;)+&mgr;
em
)·
E
app
].  (8)
Equation 4 gives a function of &zgr; which includes a term for surface charge (&sgr;
si
+&sgr;
rv
) for both the chemically-generated surface charge and the external voltage-induced charge. For the surface coating assessments &sgr;
rv
=0 and &sgr;
si
is a function of the surface coating. It follows that upon coating the surface, the measured change in elution time can be used directly to calculate the change in the surface charge from the following equation:
&Dgr;
t
el
=L
/[({exp(−&kgr;
x
)·(2
kT/ze
)·sin
h
−1
[(&Dgr;&sgr;
si
)/(8
kT&egr;
b
n
0
)
½
]·(&egr;
b
/&eegr;)}+&mgr;
em
)·
E
app
]  (9)
or by substituting A=exp(−&kgr;x)(&egr;
b
/&eegr;)(2kT/ze) and B=1/(8kT&egr;
b
n
0
)
½
this simplifies to:
&Dgr;
t
el
=L
/[(
A
·sin
h
−1
[B&Dgr;&sgr;
si
]+&mgr;
em
)·
E
app
].  (10)
Noting that all variables in this expression except &Dgr;t
el
are constant under these experimental conditions and rearrangement results in a more useful form of this equality:
&Dgr;&sgr;
si
=[sin
h
{([
L
/(&Dgr;
t
el
E
app
)]−&mgr;
em
)/
A}]/B.
  (11)
However, the usefulness of the external voltage technique is limited because it only provides control at low pH (e.g., less than pH 5) and low ionic strength buffers in standard systems.
External voltage to control

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