an apparatus for electrochemical analysis of fluids is provided that can be adapted to be compact in size , economic to manufacture , and convenient to deploy . exemplary embodiments of apparatus for electrochemical analysis of fluids include a chamber having a depth dimension for accommodating a volume of a fluid under test , and a pair of electrodes disposed within the chamber and extending along the depth dimension thereof in laterally spaced relation to each other . a soluble solid is disposed within the chamber between the electrodes , occupying a lateral gap therebetween to an extent of at least a portion of the depth dimension of the chamber . a rate of dissolution of the soluble solid within the fluid is at least partially dependent on a chemical concentration of a corresponding analyte present in solution in the fluid to the extent that the soluble solid dissolves in the fluid , the fluid fills the void generated by the dissolving solid . because the soluble solid is a poorer conductor compared to the fluid , dissolution of the soluble solid leads to an increase of conductance between the electrodes . the rate of conductance change further depends on the properties of the dissolving solid and the actual analyte concentration in solution in the fluid . materials suitable for use with respect to the soluble solid according to the present disclosure include commercially available materials that exhibit respective solubilities dependent on the concentration in solution of a chemical component or active species of interest , e . g ., h + concentration ( i . e ., ph ), proteins , amino acids , glucose , enzymes and other analytes of interest . exemplary materials for use with respect to the soluble solid according to the present disclosure include polymers that exhibit a ph - dependent dissolution rate , such as eudragit acrylic polymers manufactured by degussa gmbh , and polymers that exhibit dissolution rates that are dependent on the presence of colon enzyme , such as azo polymers used by alizyme pic ( cambridge , united kingdom ). apparatus and methods for electrochemical analysis of fluids in accordance with the present disclosure may be used to measure the concentration for a large number of chemical components present within a fluid under test . in embodiments of the present disclosure , such apparatus and methods rely on polymers with specific solubility depending on concentration of compounds mixed within the fluid , and include an electronic device that allows an accurate measurement of the solubility based upon complex conductance measurements . the lifetime of the electronic device may be limited in accordance with embodiments of the present disclosure , and controlled by processing parameters of the device . in accordance with some embodiments of the present disclosure , a small , simple , energy efficient ‘ lab - on - a - chip ’ solution is provided having a response time in the field at least comparable to , if not superior to , many larger , more bulky systems commonly limited to use within a laboratory . such an apparatus can be implemented through the use of an integrated circuit ( ic ) electronic device combined with an array of confined micro - cylinders fabricated via mems processes at the surface of a die associated with the ic electronic device , and filled with polymers having known etching rate versus chemical concentration of active species in solution in the fluid under test . for illustration purposes , the disclosed apparatus and methods are described in greater detail herein with reference to a tool for measuring analyte concentration in solution in a fluid under test . however , the disclosed systems and methods have wide ranging applicability , as will be readily apparent to persons skilled in the art , including implementations directed to a variety of analytes . thus , in one exemplary embodiment of the present disclosure , the apparatus includes a soluble solid in the form of a polymer that does not dissolve until the ph is above a threshold value and , as a result , the conductance between the electrodes does not increase unless the fluid under test has a ph above this threshold . if the ph of the fluid under test is above the applicable threshold , the conductance between electrodes will advantageously increase proportionally to the difference between the actual ph value of the fluid under test and the lower threshold ph of the soluble polymer . additionally , in one exemplary embodiment of the present disclosure , the apparatus includes a soluble solid in the form of a polymer that does not dissolve unless the ph of the fluid under test is below a threshold value and , as a result , the conductance between the electrodes does not increase unless the fluid under test has a ph below this threshold . if the ph of the fluid under test is below the applicable threshold , the conductance between electrodes will advantageously increase proportionally to the difference between the actual ph value of the fluid under test and the higher threshold ph of the soluble polymer . therefore , by monitoring a rate of change in conductance between the electrodes between which the soluble solid is disposed , either or both of a ph limit value and an actual ph value can be derived . when an apparatus for electrochemically analyzing a fluid based on this principle of concentration - dependent solubility is used , conductance between each pair of electrodes may be measured as a function of time , and the rate of conductance change may be used to derive the concentration value of the analyte present in solution in the fluid under test . one unique advantage of such an apparatus for electrochemically analyzing a fluid is that the apparatus can be operated without absolute calibration . variation in manufacturing process and environmental conditions , such as overall conductivity of the fluids under test , can cause variation in absolute conductance between electrodes . these variations , however , do not interfere with derivation of the concentration value of an analyte present in solution in a fluid under test because the concentration value is determined by the change rate of conductance , not by the absolute value of conductance . of course , such an apparatus can be used in conjunction with a reference electrode to account for environmental changes in the rate of conductance . an apparatus 100 for measuring analyte concentration in solution in a fluid under test in accordance with embodiments of the present disclosure is shown in fig1 . the apparatus 100 may include a silicon - based integrated circuit ( ic ) 102 . the ic 102 may incorporate an input / output ( io ) data block 104 , a data processor and control unit ( dpcu ) 106 , an amplitude and frequency control unit ( afcu ) 108 , a complex admittance measurement unit ( camu ) 110 , and an electrode selector ( es ) 112 . the apparatus 100 may further include an electrode array ( ea ) 114 . the io 104 may be an interface of the circuit with respect to external devices . the ea 114 is a matrix of electrodes present at an upper margin or surface of the ic 102 . each of the electrodes of the ea 114 can be connected through the es 112 block to corresponding measurement ports of the camu 110 . all other electrodes of the ea 114 may be grounded . the es 112 may be an array of analog switches which allows the selection of a single electrode out of the ea 114 . the camu 110 can measure the complex admittance of the circuit connected at the selected electrode from the ea 114 . the frequency and amplitude of the test signal can be controlled and / or imposed by the afcu 108 . the dpcu 106 may receive analog signals provided by the camu 110 and convert the same to digital values . the dpcu 106 may further store and / or process such digital values , take decisions regarding the frequencies and amplitudes of operations from the afcu 108 and operate the es 112 accordingly . the dpcu 106 may further be employed to transfer to the io 104 measurement results with respect to concentration ( s ) of one or more analytes present in solution in the fluid under test . in accordance with embodiments of the present disclosure , the cmos die 200 shown in fig2 can embody the fig1 ic 102 . for example , the cmos die 200 may include an upper margin 202 featuring an array of peripherally - disposed contacts 204 associated with an input / output interface of the circuit ( e . g ., associated with the fig1 io 104 ). a mems process may be utilized to modify and / or convert the cmos die 200 of fig2 to form an embodiment of the fig1 apparatus 100 in accordance with the present disclosure . an example of such a process is shown and described below with reference to fig3 - 13 . referring now to fig3 , 4 and 5 , a modified cmos die 300 can be formed by modifying the fig2 cmos die 102 via conventional metal deposition process and associated appropriate patterning to form a contact pattern 302 on an upper margin 304 of the die 300 operative to permit electrical interconnection between an ic ( e . g ., fig1 ic 102 ) and an electrode array ( e . g ., fig1 ea 114 ) in accordance with the present invention . referring now to fig6 , 7 and 8 , a modified cmos die 600 can be formed by further modifying the fig3 modified cmos die 300 via an appropriate aluminum - silicon deposition and etch processes ( e . g ., with a highly selective rie ) to form a mask 602 . the mask 602 may include an array of chambers 604 for accommodating small volumes of a liquid under test , each of which may include a cylindrically shaped microbarrel 606 connected to ground and a column shaped central electrode 608 . the central electrodes 608 may be disposed within the microbarrels 606 , and , further may be coaxial with , and / or coextensive ( e . g ., depthwise ) therewith . referring now to fig9 , 10 and 11 , a modified cmos die 900 can be formed by further modifying the fig6 modified cmos die 600 via an appropriate material layer deposition and etch process , e . g ., to form a dielectric material layer 902 atop the fig6 mask 602 . for example , the dielectric material layer 902 may be a sio 2 - si 3 n 4 layer . one or more of the fig6 chambers 604 may be masked during this step so as to prevent the dielectric material layer 902 from extending thereto . for example , four such chambers ( e . g ., chambers lacking a layer 902 of a dielectric material ) may be positioned on respective corners 904 , 906 , 908 , 910 of the die 900 , and / or may be used to measure air admittance ( e . g ., as part of a measurement control function ). referring now to fig1 and 13 , an analyte concentration measurement tool 1200 is shown . for example , the tool 1200 may be implemented to embody the analyte concentration measurement tool 100 of fig1 . the tool 1200 can be formed by further modifying the fig9 modified cmos die 900 via filling one or more of the fig6 chambers 604 with similar and / or different polymers and executing an appropriate annealing process to form fluid - polymer filled cylinders or chambers 1202 ( described further hereinbelow ), wherein the dissolution rate of each such polymer may be specific to one or more of the same or different chemical compounds in solution in a fluid under test . the fig9 corner - disposed chambers 904 , 906 , 908 , 910 may be left unfilled with polymer for purposes of measuring air admittance as part of a measurement control function . likewise , an entire row 1204 of chambers 1206 , also referred to herein as fluid filled cylinders or chambers 1206 , may be left unfilled with polymer for purposes of measuring an admittance of the fluid under test as described more fully below . the tool 1200 includes an ic 1208 which can embody , for example , the fig1 ic 102 , and a mems region 1210 which can embody the fig1 ea 114 . the mems region 1210 can be configured to be exposed to the fluid under test , while the ic 1208 can be configured such that its internally - disposed electrical circuitry and / or functions are secured from damage from the fluid under test . referring now to fig1 , when exposed to fluid 1400 from the fluid under test , the soluble solid 1402 ( e . g ., polymer ) within the chamber 1202 is dissolved by the analyte present in solution in the fluid under test . fig1 gives a vertical plane cross - section through a fluid - polymer filled cylinder ( fpc ) 1202 after the soluble solid 1402 contained therein was etched to an etch value equal to h fluid . fig1 gives a vertical plane cross - section through a fluid filled cylinder ( fc ) 1206 . when exposed to the fluid under test , the fluid - filled cylinders 1206 , containing no soluble solid ( e . g ., containing no polymer ), are filled with fluid 1500 . the fig1 tool 1200 measures the complex admittances for all of the fpcs 1202 and fcs 1206 of the mems region 1210 at specific time intervals and estimates the electrical properties of polymers within the fpcs 1202 and the fluid within the fcs 1206 and the etch rate for every type of polymer from every fpc 1202 . based on the etching rate , one may determine the concentrations of active chemical species within the fluid under test . the capacity to make such determinations may last as long as the polymers within the fpcs 1202 are not completely dissolved within the fluid under test . exemplary electric equivalent circuits 1600 , 1700 for fpcs 1202 and fcs 1206 are given , respectively , in fig1 and 17 . the below - described algorithm is executable by a processor ( e . g ., by the fig1 dpcu 106 ) in accordance with the present disclosure to allow the determination at a time t j of the concentration of species present in solution in the fluid under test , given the fpc 1202 are filled with different polymers with etching rates specific to every chemical concentration of the species . v probe is a voltage source v probe = v 0 e i ( oω + φ ) with i =√{ square root over (− 1 )}, v 0 : amplitude , ω : angular frequency , φ : phase , t : time . the complex impedance of the circuit from fig8 ( seen by the voltage source voltage source v probe ) is : and the resistors are not frequency dependent ( the voltage source frequency is smaller than the minimum ionic rotation frequency within the fluid or polymer ). capacitances and resistances are calculated with the coaxial model . as a reminder : the resistance measured between the inner electrode with radius r 1 and output electrode with radius r o of a coaxial cable of length l filled with a material of resistivity ρ is : the capacitance measured between the inner electrode with radius r 1 and output electrode with radius r o of a coaxial cable of length l filled with a material with relative dielectric constant ε dielectric is : interestingly enough , the time constant associated to this coax cable is independent of any geometrical parameters of the cable : τ = r ( l ) c ( l )= ε dielectric ε 0 ρ ( 5 ) measuring the admittance y c , test , air of the test cylinders in air ( ε air = 1 ) allows the experimental determination of the thickness of the dielectrics within the fpc and fc : the admittance of the fc filled with air is ( ρ air ≈∞, ε air = 1 ) the measurements performed in air allowed the determinations of two critical values : ε dielectric and t dielectric replace the values for x cpe — t and x cpt — o with the expressions given in ( 7 ) for h fluid = 0 : step 2 : measure the fluid and polymer admittance at any time after the device has been immersed in a fluid . assume the fluid etched the polymer , and got to the coordinate h fluid of the fpc . with this complex impedance measurement approach , the etching of the polymer within a fpc h fluid is calculated based on the initial values of the impedance of the fpc ( fpc in air ) and the adjacent fpc measurement . this does not solve the variations of the polymer electrical parameters vs . time . let us look at a frequency swipe method : for the same h fluid the frequency of the measurement of the ama is changed within limits larger than the poles and zeros of the complex admittance . from the bode plot of the absolute value of the complex impedance of an fc , one can extract τ fluid + τ df and τ fluid which is equivalent to resolving ρ fluid and ε fluid . we will use the same procedure for extracting the parameters of the polymer within an fpc : the poles and zeros for y g , fpc can be estimated from the bode plot of ∥{ tilde over ( y )} g , fpc ∥, therefore one can extract ρ polymer and ε polymer at any time during the measurement of the fluid . let us consider an admittance measurement array ( ama ) as described above , with the following characteristics : confines a ( not necessarily ) square array of n cylinders × n cylinders cylinders . 4 cylinders of the ama are not covered with si 3 n 4 sio 2 dielectrics and are used to measure ( in air ) the specifics of the dielectric covering the a1 electrodes ( ε dielectric , τ dielectric ). n cylinder = n fc , cylinder cylinders ( different from the 4 above ) are not filled with any polymers . n polymer = n cylinders × n cylinders − n fc , cylinder − 4 cylinders are filled with n polymer different types of polymers . every polymer is chemically sensitive to a specific chemical species within the fluid under test . for example , assume the fluid under test confines n specie active species with concentrations c specie . the polymer in cylinder k ∈≦{ 1 , . . . , n polymer }⊂ n reacts with the active species within the fluid . as a result of the reactions , the polymer will become soluble within the solution . the rate of solubility is related to the etching rate of the polymer with a function isomorphic with : r ks = m ks ( c s − c ks , threshold ) θ ( c s − c ks , threshold )∀ k ={ 1 , . . . , n polymer },∀ s ={ 1 , . . . , n species } ( 20 ) r ks etching rate of polymer k reacting with specie s θ ( c s − c ks , threshold ) heaviside function of difference between active specie concentration c s and concentration threshold c ks , threshold above which polymer k reacts with specie s m ks ( c s − c ks , threshold ) increasingly monotonic function describing the etching rate of polymer k by specie s of concentration c s the total etch rate for polymer k while reacting to all species n specie within the fluid is the sum of the etch rate of the polymer per specie : with m kt ( c i − c ks , threshold )= m ks ( c s − c ks , threshold ) θ ( c s − c ks , threshold ). the ama structure is measured in air and the specifics of all n polymer are stored as ( ε k , ρ k , τ ksf ),∀ k ={ 1 , . . . , n polymer }. the ama structure immersed in the solution under test . we will assume at any time there is no concentration gradient of any active species at the surface of the ama , therefore all cylinders “ see ” at the same time the same value of the concentration value for any species . the admittance measurement circuit measures for every cylinder ( fluid polymer filled cylinders ( fpf ) and fluid - filled cylinders ( fc )) at a sample rate s all complex admittances and calculates : the average values of ( ε fc , fluid ( t j ) , ρ fc , fluid ( t j ) , τ fc , fluid ( t j ) ) at time t j : based upon the values obtained above , and assuming the fluid parameters within adjacent fc and pfc are the same ( no concentration gradient at the surface of the ama ), calculate for every fpc we can approximate the etching rate at time t j as : r [ n polymer , 1 ] ( t j ) =[[ r k ( t j ) ]], measured etching rate matrix , at time t j c [ 1 , n specie ] ( t j ) =[[ c r ( t j ) ]], concentration matrixal time t j , to be determined c t11 [ n polymer , n specie ] =[[ c ki , threshold ]], concentration threshold for polymer k reacting with specie i , known m [ n polymer , n specie ] ( c )=[[ m jk ( c ik )]], etching rate function matix for polymer k reacting with specie i , known c n [ n polymer , n specie ] ( t j ) = 1 [ n polymer , 1 ] c [ 1 , n specie ] ( t j ) − c th [ n polymer , n specie ] , normalized concentration matrix ( 25 ) r [ n polymer , 1 ] ( t j ) = m [ n polymer , n specie ] ( c n [ n polymer , n specie ] ( t j ) ) 1 [ n specie , 1 ] ( 26 ) for the case when the matrix m [ n polymer , n specie ] is has an inverse , i . e . n polymer = n species = n e , the equation reads : r [ n e , 1 ] ( t j ) = m [ n e , n o ] ( c n [ n p , n t ] ( t j ) ) 1 [ n e , 1 ] ( 27 ) m [ n e , n e ] − 1 ( 1 [ n e , 1 ] c [ 1 , n e ] ( t j ) − c th [ n e , n e ] ) r [ n e , 1 ] ( t j ) = 1 [ n e , 1 ] ( 28 ) this represents a system of n e equations with n e unknowns c [ 1 , ne ] ( t j ) , which shall have a unique solution , as long as the matrix m [ n e , n e ] is inverseable . although the invention is illustrated and described herein with reference to specific embodiments , the invention is not intended to be limited to the details shown . rather , various modifications may be made in the details within the scope and range of equivalents of the claims and without departing from the invention .
an apparatus and method for electrochemical fluid analysis comprises a chamber having a depth dimension for accommodating a volume of a fluid under test , first and second electrodes disposed within the chamber and extending along the depth dimension in spaced relation with each other , and a soluble solid , such as an annealed polymer , e . g . eudragit occupying a lateral gap between the first and second electrodes . the rate of dissolution as monitored by electrochemical impedance spectroscopy of the soluble solid within the fluid depends on the chemical concentration of a corresponding analyte present in solution in the fluid . in one embodiment a silicon - based integrated circuit device defining an upper margin includes an array of electrodes disposed along said upper margin to permit direct exposure of the electrode array to the fluid under test . the device is constructed using cmos technology .