Abstract:
A device is provided for cooling or heating vessels and containers for carrying out chemical or physical reactions. The device includes the following components in a vertical direction from top to bottom: a heat-conductive cooling or heating plate; at least one Peltier element equipped with electrical connections; optionally at least one heat-conductive separator plate between two Peltier elements respectively; a heat-conductive thermoblock, through which one or more fluid channels pass, for dissipation and supply of heat from and to the at least one Peltier element; and an external control unit for the at least one Peltier element. The components rest on top of one another and are therefore in direct planar contact with one another.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application is a Section 371 of International Application No. PCT/AT2012/050093, filed Jul. 4, 2012, which was published in the German language on Jan. 17, 2013, under International Publication No. WO 2013/006878 A1 and the disclosure of which is incorporated herein by reference. 
     
    
     BACKGROUND OF THE INVENTION 
       [0002]    The present invention relates to a device for cooling or heating vessels and containers for carrying out chemical or physical reactions, making use of the Peltier effect. 
         [0003]    The Peltier effect describes the phenomenon that in a current-carrying pair of thermocouples made of different materials (“Peltier element”), one of the thermocouples becomes cold, while the other one becomes warm. Thus, when using Peltier elements as cooling or heating devices, on the side facing away from the object to be cooled or heated, i.e. the “backside” of the Peltier element, heat has to be withdrawn during cooling operation, while heat has to be supplied during heating operation. Usually, this heat compensation occurs through ambient air. 
         [0004]    Various devices using Peltier elements for heating or cooling reaction vessels are known. For example, heating blocks with Peltier modules are available from the company Bio Integrated Solutions, Inc., which are calibrated for use at temperatures between −10° C. and +120° C. (see their website: http://www.biointsol.com/products.aspx?product=7). 
         [0005]    In patent literature, for example, International patent application Publication No. WO 01/05497 A1 and U.S. Pat. No. 4,950,608 each describe a cooling or heating device comprising a heat-conductive plate and a thermoblock provided with fluid channels as well as elements of a resistance heater and having an external control unit. However, none of the two documents mentions a Peltier element. 
         [0006]    U.S. patent application publication No. 2008/286171 A1 describes a comparable device, however, mentions additionally that the fluid flowing through the channels can be cooled by Peltier elements—which due to the design have to be positioned outside. 
         [0007]    German published patent application DE 10 2007 057 651 A1 discloses a system for controlling the temperature of samples consisting of a series of heat-conductive sample receiving blocks with a plurality of recesses for test tubes and temperature control blocks, which preferably contain Peltier elements, so that a temperature control block can show a heating effect in one direction and simultaneously a cooling effect in another direction. Direct transmission of heat between the temperature control blocks is not envisaged. The overall temperature of the device is to remain constant, i.e. there is no heat dissipated to the outside nor supplied from the outside, while the Peltier elements alternately provide heating and cooling effects to the samples by switching the current direction. 
         [0008]    International patent application Publication No. WO 98/50147 A1 discloses a system for carrying out chemical reactions under heating or cooling by Peltier elements. Therein, two Peltier elements are provided on two sides of a reaction block having recesses for samples. Both Peltier elements are in contact with one thermoblock each on the side facing away from the reaction block, which thermoblock is to serve as heat storage. During operation, the Peltier elements either transmit heat from the reaction block to the two thermoblocks or vice versa. Again, there is no (substantial) heat withdrawn from the system nor supplied to the same. 
         [0009]    German published patent application DE 35 25 860 A1 describes a thermostat with a metal block having receptive borings for sample containers to which a heating or cooling device in the form of Peltier elements is mounted. Therein, either only one single Peltier element is provided at the bottom side of the block or additional Peltier elements are fixed to the sides of the block. The possible temperature range mentioned is −60° C. to +60° C., there is, however, no evidence because there are no specific working examples at all. 
         [0010]    The disadvantage of embodiments using ambient air is that heat compensation on the backside of the Peltier element occurs very slowly. By providing fans for air supply the effect can be improved slightly, but the results are not satisfactory, in particular in cooling operation. That is, the temperatures desired for low-temperature reactions, for example in chemical laboratories, are not achieved, such as temperatures in the range of those of ice/saline mixtures, i.e. of −20° C. or below, or those of dry ice freezing mixtures, i.e. in the range of −70° C. In addition, the fans sometimes create a lot of noise. 
         [0011]    German published patent application DE 2 013 973 A1 discloses a thermostat that can be thermally influenced by several Peltier aggregates arranged side by side. For cooling, a heat exchanger is provided on the backside of the Peltier aggregates, which can be operated either by water or air cooling. Here, air cooling is to set in when water cooling fails, to which purpose, again, preferably a fan is provided that can be switched on if needed. This air cooling is to guarantee that “long-term investigations can be conducted without continuous monitoring, without the risk of interruptions”. Obviously, water cooling (and optionally fan-supported) air cooling are seen as equivalent. The temperatures achievable with such thermostats are not mentioned. 
         [0012]    Thus, German published patent application DE 20 13 973 A1 is not able to solve the above problem of providing low temperatures in a reaction block by Peltier elements, the optional fan causes a certain noise level, and in addition, the thermostat disclosed in that document would not be suitable for continuous operation in the heating mode because heat supply from the ambient air is not sufficient for this. 
       BRIEF SUMMARY OF THE INVENTION 
       [0013]    Consequently, the object of the invention was to provide a device by which the above problem of being able to cool a reaction block to very low temperatures and heat it with one and the same device can be solved. 
         [0014]    Contrary to the state of the art, the inventors of the present subject matter have found out and proven in the course of their research that water and air cooling are not equivalent, but that water cooling leads to substantial improvements in the performance of Peltier elements, especially in cases in which several Peltier elements are arranged side by side or, in particular, one above the other. 
         [0015]    Thus, the invention relates to a device for cooling or heating vessels and containers for carrying out chemical or physical reactions, including tubular reactors, such as capillary reactors, the device comprising the following components in a vertical direction from top to bottom:
       a heat-conductive cooling or heating plate;   at least one Peltier element equipped with electrical connections;   optionally at least one heat-conductive separator plate between each two Peltier elements;   a heat-conductive thermoblock, through which one or more fluid channels pass, for dissipation and supply of heat from and to the at least one Peltier element; and   an external control unit for the at least one Peltier element;
 
wherein the cooling or heating plate, the Peltier element(s), the optional separator plate and the thermoblock rest on top of one another and are therefore in direct, full-faced contact.
       
 
         [0021]    By providing a thermoblock with continuous liquid cooling or heating for one or more Peltier elements that are in full-faced contact with the thermoblock and the cooling or heating plate arranged thereabove in combination with the control unit for the supplied electric energy, the performance of the overall device was improved, as is described in detail in the examples below. Even the simplest embodiment of the invention with only one single Peltier element provided temperatures below −30° C. during cooling operation. 
         [0022]    In addition, temperature changes, for example switching from cooling to heating operation, can be implemented substantially faster with the liquid cooling, in particular when the liquid used as cooling or heating medium is precooled or preheated outside of the device, where air cooling or heating would require extensive equipment and entail high costs because of the substantially poorer thermal properties. Of course, for economic reasons the liquid medium used is preferably water. 
         [0023]    Specifically, when several Peltier elements are used, which rest on the thermoblock side by side and/or one on top of the other—the number of elements arranged side by side or one above the other not being specifically limited and depending, among other things, on the respectively desired dimensions and geometry—this temperature can be substantially shifted further down. With a two-stage embodiment, i.e. with Peltier elements one above the other, cooling temperatures around −70° C. were achieved. 
         [0024]    In the latter embodiments with two or more Peltier elements arranged one above the other, each Peltier element serves for heat compensation for the above element. Here, the elements are preferably separated from each other by a heat-conductive separator plate with which they are in direct, full-faced contact, in order to avoid direct electric contact. 
         [0025]    Furthermore, the actual Peltier elements are preferably each embedded in a plate of a material that provides the element with electric insulation against the outside and thermal protection against external influences, preferably cork. In addition to the electric insulation, the heat flow is thus concentrated in a vertical direction and the elements are protected against damage. 
         [0026]    According to the present invention, a block can be stacked on the cooling or heating plate, in which one or more recesses for receiving reaction vessels or containers can be provided, or the plate itself is a block, which again can have corresponding recesses. Consequently, the device is adaptable to various reaction vessels and containers with high variability. 
         [0027]    For the purpose of the present invention, reaction vessels and containers refers to any receptacle in which chemical or physical reactions can take place, including sample tubes, flasks, bottles, microtiter plates, tubular or pipe reactors, for example capillary reactors, etc., without being limited thereto. 
         [0028]    In some preferred embodiments of the invention, the chemical or physical reactions can take place directly in “recesses” of the blocks, i.e. the stackable block or the cooling or heating plate provided as a block itself can serve as a reaction vessel. Provided as a tubular reactor, i.e. with a more or less thin, continuous channel, the block can serve as a flow-through cell. 
         [0029]    The fluid channels in the thermoblock, the recesses in the cooling or heating plate provided as a block or those in a block to be stacked on the plate are preferably bores or cutouts provided therein. These can be produced in a simple and inexpensive manner. 
         [0030]    The materials for the components of the device are not specifically limited as long as sufficient heat conduction from one component to the other is guaranteed. In view of heat conductivity, the cooling or heating plate, the thermoblock and optionally the separator plate are preferably made of aluminum, copper or alloys of these metals, with aluminum and its alloys being particularly preferred. Alloys are preferably those with non-ferromagnetic alloy partners. 
         [0031]    However, in cases in which the cooling or heating plate is provided as a reaction block, it can, for example, also consist of other alloys, for example stainless steel or Hastelloy, of glass or of plastics, for example polytetrafluoroethylene or polyamide. These are characterized by substantially lower heat conductivities than aluminum or copper, however, they are far more inert towards the reactions to be conducted therein. Optionally, the heat conductivity of the material can be increased by doping or additives, for example metal powder or chips, which is particularly easy with plastics. The same material options also apply to a separate reaction block to be stacked on the plate. 
         [0032]    In preferred embodiments of the invention, a heat transfer promoting medium is provided between individual components of the device in order to further increase the performance. It is not particularly limited and can, for example, comprise any known heat conduction paste, fluid and the like, such as zinc oxide or silicone oils containing aluminum, copper or silver components, without being limited thereto. 
         [0033]    Preferably, the individual components resting on top of one another are adhered or screwed, in particular screwed, to each other in order to prevent displacement. When using a heat conducting paste or the like, it can simultaneously serve as adhesive. 
         [0034]    Furthermore, in preferred embodiments of the inventive device, the edges of the components resting on top of one another are in true alignment with each other in order to minimize the surface of the overall device and to reduce heat exchange with the environment. The cross-sectional shape of the device and of the individual components is in general not particularly limited. Particularly useful, however, are rectangular or square shapes because they are easy to manufacture and store as well as a circular shape for reasons of surface minimization. The shape of either only the cooling or heating plate or also that of other components can be adapted to conventional laboratory apparatus or reaction vessels. 
         [0035]    Also, in preferred embodiments of the device, pipe or tube connections are provided at external ends of the fluid channels in the thermoblock in order to guarantee easy and quick start-up and safe operation. 
         [0036]    Below, the invention will be described in further detail in specific exemplary embodiments with reference to the accompanying drawings. 
     
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS 
         [0037]    The foregoing summary, as well as the following detailed description of the invention, will be better understood when read in conjunction with the appended drawings. For the purpose of illustrating the invention, there are shown in the drawings embodiments which are presently preferred. It should be understood, however, that the invention is not limited to the precise arrangements and instrumentalities shown. In the drawings: 
           [0038]      FIG. 1  shows a lateral view of a simple embodiment of the inventive device. 
           [0039]      FIG. 2  shows an isometric view of the embodiment of  FIG. 1 . 
           [0040]      FIG. 3  shows an isometric exploded view diagonally from above of the embodiment of  FIGS. 1 and 2 . 
           [0041]      FIG. 4  shows an isometric exploded view diagonally from below of the embodiment of  FIGS. 1 and 3 . 
           [0042]      FIG. 5  shows a side view of another embodiment of the inventive device. 
           [0043]      FIG. 6  shows an isometric view of another embodiment. 
           [0044]      FIG. 7  shows an isometric exploded view diagonally from above of the embodiment of  FIG. 6 . 
           [0045]      FIG. 8  shows an isometric exploded view diagonally from below of the embodiment of  FIGS. 6 and 7 . 
           [0046]      FIG. 9  shows an isometric view of a block for receiving reaction vessels. 
           [0047]      FIG. 10  shows an isometric view of a block for receiving tubular reactors. 
           [0048]      FIG. 11  shows an isometric view of another block for receiving a tubular reactor. 
           [0049]      FIG. 12  shows a graphic representation of the measured values obtained in Example 1 using a device according to an emodiment of the present invention. 
           [0050]      FIG. 13  shows a graphic representation of the computer-simulated values used in Example 2 for the device from Example 1. 
           [0051]      FIG. 14  shows a graphic representation of the computer-simulated values of Example 3 for a two-stage device. 
           [0052]      FIG. 15  shows a graphic representation of the computer-simulated values for the two-stage device of Example 3 in case of a two-dimensional simulation. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0053]      FIG. 1  shows a simple embodiment of the cooling/heating device of the invention. A cooling or heating plate  1  is shown at the top, in which an opening  10  for receiving a temperature sensor (not shown) is provided, which is, for example,. a simple thermometer or preferably a thermoindicator connected with the control unit (not shown) for the Peltier element. 
         [0054]    A Peltier element  2  lies under the plate  1 , which is provided with electric connections  7  for connection with the control element. Preferably, the Peltier element is embedded in a plate of a material that provides the element with thermal and electric insulation to the outside, i.e. to the side. To increase the cooling or heating performance, one or more further Peltier elements can be provided in addition to the Peltier element  2  (which is not shown in  FIG. 1 ). 
         [0055]    The thermoblock  6  is arranged under the Peltier element  2 , which consists of two parts in preferred embodiments, i.e. comprises an upper part  6   a  and a lower part  6   b.  This facilitates its production because the fluid channels  8  running within the thermoblock are easier to produce by (computer-controlled) milling in only one or in both parts.  FIG. 1  shows the inlet and outlet openings of a fluid channel  8 . However, a thermoblock can also be provided with several separate channels to be supplied with a fluid. 
         [0056]    Preferably, a heat conducting medium (not shown) is provided between the individual components 1 to 6 resting on top of one another in order to improve heat transfer. The edges of the individual components are in true alignment with each other in order to keep the surface and thus the heat exchange with the environment small. 
         [0057]      FIG. 2  shows an isometric view of the same embodiment in which, in addition to  FIG. 1 , also an opening  10  for a temperature sensor as well as screws  11  for a stable connection of the individual components with each other are shown, wherein the screws are preferably enveloped with sleeves (not shown), for example of polyamide or other plastics, to provide thermal insulation. 
         [0058]      FIG. 3  shows an isometric exploded view diagonally from above of the same embodiment. In addition to the two previous drawings, this figure furthermore shows bottom screws  11  as well as the fact that the Peltier elements  2  consist of two parts. That is, the actual Peltier element  2   a  is embedded in a plate  2   b  of a material, such as plastic or preferably cork, which not only provides the element with external thermal and electric insulation, but also protects it against mechanical or chemical damages. 
         [0059]      FIG. 4  shows an isometric exploded view diagonally from below of the same embodiment again. In addition, a preferred course of the liquid channel  8  in the interior of the upper part  6   a  of the thermoblock may be seen. Specifically, the channel  8  preferably runs through the thermoblock in a serpentine or meandering manner in order to provide good heat transfer from the thermoblock to the liquid or vice versa. In  FIG. 4 , it can be seen that the channel enters and leaves the thermoblock  6  on the same side. What is indicated is, assuming that liquid enters through the opening marked with  8   a  into the left half of the thermoblock, a meandering course of the channel  8  to the opposite side, where it switches to the right half of the thermoblock, after which the channel  8  meanders back to the front side and the outlet opening  8   b.    
         [0060]      FIG. 5  shows a lateral view of a two-stage embodiment of the inventive device with two Peltier elements, wherein another Peltier element  4  is provided between the cooling or heating plate  1  and the Peltier element  2  and a heat conducting separating  5  is provided between the Peltier elements. This separator plate avoids direct electrical contact between the Peltier elements  2  and  4  and at the same time promotes heat transfer from one to the other. In this embodiment, the lower Peltier element  2  serves for cooling or heating the upper element  4  and is itself cooled or heated by the again two-part thermoblock  6   a,    6   b.    
         [0061]      FIG. 6  shows an isometric lateral view of another two-stage embodiment with three Peltier elements. In the lower plane, another Peltier element  3  is provided in addition to element  2 . On these two, a separator plate  5  and a central Peltier element  4  rest. This particularly increases heat exchange between the Peltier elements  2  and  3  in the lower plane and the thermoblock. 
         [0062]      FIG. 7  shows an isometric exploded view diagonally from above of the embodiment of  FIG. 6  in which the preferred two-part design of the Peltier elements  2  to  4 , in particular of element  4 , is shown. The latter again consists of an element  4   a  embedded in an insulating plate  4   b.    
         [0063]      FIG. 8  shows an isometric exploded view diagonally from below of the embodiment of  FIGS. 6 and 7 . Again, the serpentine or meandering course of the fluid channel  8  through the thermoblock is indicated. 
         [0064]      FIGS. 9 to 11  show possible embodiments of blocks of the inventive device for receiving reaction vessels. This can either be a cooling or heating plate provided as a block or a separate “reaction block” to be stacked thereon. In both cases, the respective component is again connected with one or more components underneath by screws  11  and preferably has an opening  10  for a temperature sensor. 
         [0065]    In  FIG. 9 , this block  14  has circular recesses  9  in which individual reaction vessels (not shown), such as flasks, bottles, reaction tubes and the like, can be received and thus cooled or heated. 
         [0066]      FIG. 10  shows a cylindrical block serving as holder for a tubular or pipe reactor (not shown), for example a capillary reactor. During operation, the latter is simply wrapped around the cylinder. However, embodiments with a partly or completely hollow and not necessarily cylindrical block are also possible, into which reaction vessels, for example also capillary reactors, can be placed. 
         [0067]      FIG. 11  shows a thermoblock with a spiral-shaped recess, for example cutout, into which a tubular reactor, for example a capillary reactor, can be placed. During operation, such a block can be provided with a cover plate in order to prevent heat exchange with the environment and thus guarantee a constant temperature of the reactor. Such a cover plate can be completely planar or also have a recess, which is preferably mirror-inverted with regard to the recess  9  in the block itself and can be registered with the latter. In this case, the two recesses together define, as it were, a heating or cooling channel for the tubular reactor, whose entire surface is thus in contact with the block or cover plate, which greatly improves heat transfer. The material of such a cover plate is not particularly limited, and in case of a planar plate it can be glass, for example, while a plate provided with a recess mirror-inverted with regard to the block preferably consists of the same material as the thermoblock itself, for example aluminum. 
         [0068]    As mentioned above, such blocks can also directly serve as reaction vessels by allowing the chemical or physical reactions to be thermally influenced in corresponding hollow spaces, for example recesses  9 , of the reaction block. 
       EXAMPLES 
     Examples 1 and 2 
     One-Device Stage 
       [0069]    A device as shown in  FIGS. 1 to 4  was, on the one hand, produced and tested in cooling operation as described below (Example 1), on the other hand its performance was theoretically calculated in a computer simulation (Example 2). 
       Example 1  
       [0070]    Cooling plate: aluminum, 10×10×1 cm, 3.5 cm Ø bore for a temperature sensor 
         [0071]    Peltier element: TEC2H-62-62-437/75 from Eureca Messtechnik GmbH, Cologne, Germany, embedded in a cork plate with 10×10×0.3 cm 
         [0072]    Thermoblock: aluminum, 10×10×2+1 cm height; a serpentine fluid channel with a width of 6 mm, a depth of 15 mm and an overall length of 547 mm milled therein, 3.5 cm Ø bore for a temperature sensor 
         [0073]    Screwing: 17 (8+9) screws of stainless steel insulated with polyamide sleeves 
         [0074]    Temperature sensor: digital laboratory thermometer (2×), Fluke 54-II-B differential thermometer with 2×80PK-25 or 2×80PT-25 temperature probes 
         [0075]    Power supply: Current strength-controlled operation, high-performance power supply for at least 25 V/25 A 
         [0076]    The entire device (with exception of the control unit) was enveloped with polystyrene foam for thermal insulation, and the thermoblock was supplied with tap water with a temperature of 10-12° C. Subsequently, the power supply to the Peltier element was activated, and the current strength was increased in steps of 1 A. After each 5 min equilibration time, the temperature of the cooling plate and of the thermoblock was measured at the respective current strength, i.e. between 0 and 20 A, by the two thermometers. The measured values thus obtained were taken as temperature of the cold side “Tc” or temperature of the warm side “Th” of the Peltier element. 
         [0077]      FIG. 12  shows the values thus obtained with the corresponding compensation curves and their calculation principle. 
         [0078]    The lowest, continuously obtained temperature of the cooling plate at a current strength of 20 A was −31° C., which required a power of 330 W. For a short time, a temperature of −35° C. was measured at a current strength of 25 A, however, due to the power limit of the power supply used in the experiment, it could not be permanently verified. However, from the compensation curve it can be estimated that with a corresponding current strength, the lower temperature should be achievable continuously. 
         [0079]    In any case, the present invention provides a cooling device that is well suited for the use with low-temperature reactions. 
       Example 2 
       [0080]    For verification of the theoretic power limit of the inventive device of Example 1 in cooling operation, a computer simulation was conducted by using the following equation. Here, the temperature differences created by the thermopower (as defined by the Seebeck coefficient), the heat quantity created by the flow of current and the heat loss caused by the heat transfer between the cold and the warm site of the Peltier element were taken into account as follows and dynamically adapted depending on the respective temperature: 
         [0000]    
       
         
           
             Q 
             = 
             
               
                 ( 
                 
                   Se 
                   × 
                   I 
                   × 
                   T 
                 
                 ) 
               
               - 
               
                 ( 
                 
                   
                     R 
                     × 
                     
                       I 
                       2 
                     
                   
                   2 
                 
                 ) 
               
               - 
               
                 ( 
                 
                   K 
                   × 
                   Δ 
                    
                   
                       
                   
                    
                   T 
                 
                 ) 
               
             
           
         
       
     
         [0081]    Q=refrigerating capacity [W] 
         [0082]    Se=Seebeck coefficient [° K/W] 
         [0083]    I=current strength [A] 
         [0084]    T=temperature in the Peltier element [° K] 
         [0085]    R=ohmic resistance of the Peltier element [S2] 
         [0086]    K=thermal conductance of the Peltier element [W/° K] 
         [0087]    ΔT=temperature difference between warm and the cold side of the Peltier element [° K] 
         [0088]    The following coefficients were used for the calculation according to the data sheet of the Peltier element used: 
         [0089]    Se(300° K)=0.0826 V/° K 
         [0090]    R(300° K)=0.815 S2 
         [0091]    K(300° K)=3.47 W/° K 
         [0092]    Since the three coefficients above depend on the temperature in the Peltier element, the temperature dependency described in the data sheet was approximated by a fourth-degree polynomial function, which gave the following coefficients: 
         [0000]    
       
         
               
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                   
                   
               
               
                   
                 a 
                 b 
                 c 
                 d 
                 e 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                 Se(T) 
                 −1.385E−10 
                 +1.457E−07 
                 −5.812E−05 
                 +1.060E 
                 −02−6.764E−01 
               
               
                 R(T) 
                 +1.260E−08 
                 −1.348E−05 
                 +5.378E−03 
                 −9.445E 
                 −01+6.208E+01 
               
               
                 K(T) 
                 +1.074E−08 
                 −7.837E−06 
                 +1.712E−03 
                 −7.149E−02 
                  +−4.568E+00 
               
               
                   
               
             
          
         
       
     
         [0093]    For the temperature range of 225° K to 300° K, the R 2  obtained was greater than 0.999. 
         [0094]    First, Se, R and K were determined for the corresponding temperature (here T was used for the temperature on the warm side), because it is the only one known and the cold side temperature would result in a circular definition. The ΔT values were calculated by insertion into the Peltier equation. The working voltage U [V] was calculated by adding the Seebeck term and the relation U=R×I (Ohm&#39;s law). 
         [0095]    This gave the values shown in the following Table 1: 
         [0000]    
       
         
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 1 
               
               
                   
               
               
                 I 
                 Th 
                 Th 
                 Se(T) 
                 R(T) 
                 K(T) 
                 dT 
                 U 
                 Tc 
                 Pel 
                 Qw 
                 Threal 
               
               
                 [A] 
                 [° C.] 
                 [°K] 
                 [V/°K] 
                 [Ω] 
                 [W/°K] 
                 [°K] 
                 [V] 
                 [° C.] 
                 [W] 
                 [W] 
                 [° C.] 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 1.0 
                 13.0 
                 286.15 
                 0.0830 
                 0.807 
                 3.54 
                 −7.4 
                 0.2 
                 20.4 
                 0.2 
                 50.2 
                 13.0 
               
               
                 2.0 
                 13.1 
                 286.25 
                 0.0831 
                 0.808 
                 3.54 
                 −1.1 
                 1.5 
                 14.2 
                 3.0 
                 53.0 
                 13.1 
               
               
                 3.0 
                 13.2 
                 286.35 
                 0.0831 
                 0.808 
                 3.54 
                 4.7 
                 2.8 
                 8.5 
                 8.4 
                 58.4 
                 13.2 
               
               
                 4.0 
                 13.3 
                 286.45 
                 0.0831 
                 0.808 
                 3.54 
                 10.0 
                 4.1 
                 3.3 
                 16.3 
                 66.3 
                 13.3 
               
               
                 5.0 
                 13.5 
                 286.65 
                 0.0831 
                 0.809 
                 3.53 
                 14.9 
                 5.3 
                 −1.4 
                 26.4 
                 76.4 
                 13.5 
               
               
                 6.0 
                 13.8 
                 286.95 
                 0.0832 
                 0.810 
                 3.53 
                 19.5 
                 6.5 
                 −5.7 
                 38.9 
                 88.9 
                 13.8 
               
               
                 7.0 
                 14.1 
                 287.25 
                 0.0832 
                 0.810 
                 3.53 
                 23.7 
                 7.6 
                 −9.6 
                 53.5 
                 103.5 
                 14.1 
               
               
                 8.0 
                 14.4 
                 287.55 
                 0.0833 
                 0.811 
                 3.53 
                 27.6 
                 8.8 
                 −13.2 
                 70.3 
                 120.3 
                 14.4 
               
               
                 9.0 
                 14.8 
                 287.95 
                 0.0833 
                 0.812 
                 3.52 
                 31.1 
                 9.9 
                 −16.3 
                 89.2 
                 139.2 
                 14.8 
               
               
                 10.0 
                 15.2 
                 288.35 
                 0.0834 
                 0.814 
                 3.52 
                 34.4 
                 11.0 
                 −19.2 
                 110.0 
                 160.0 
                 15.2 
               
               
                 11.0 
                 15.7 
                 288.85 
                 0.0834 
                 0.815 
                 3.51 
                 37.4 
                 12.1 
                 −21.7 
                 133.0 
                 183.0 
                 15.7 
               
               
                 12.0 
                 16.2 
                 289.35 
                 0.0835 
                 0.817 
                 3.51 
                 40.2 
                 13.2 
                 −24.0 
                 157.8 
                 207.8 
                 16.2 
               
               
                 13.0 
                 16.7 
                 289.85 
                 0.0836 
                 0.818 
                 3.51 
                 42.6 
                 14.2 
                 −25.9 
                 184.6 
                 234.6 
                 16.7 
               
               
                 14.0 
                 17.3 
                 290.45 
                 0.0837 
                 0.820 
                 3.50 
                 44.9 
                 15.2 
                 −27.6 
                 213.3 
                 263.3 
                 17.3 
               
               
                 15.0 
                 17.9 
                 291.05 
                 0.0837 
                 0.822 
                 3.50 
                 47.0 
                 16.3 
                 −29.1 
                 243.8 
                 293.8 
                 17.9 
               
               
                 16.0 
                 18.5 
                 291.65 
                 0.0838 
                 0.823 
                 3.49 
                 48.8 
                 17.3 
                 −30.3 
                 276.2 
                 326.2 
                 18.5 
               
               
                 17.0 
                 19.2 
                 292.35 
                 0.0839 
                 0.825 
                 3.49 
                 50.4 
                 18.3 
                 −31.2 
                 310.5 
                 360.5 
                 19.2 
               
               
                 18.0 
                 19.9 
                 293.05 
                 0.0840 
                 0.828 
                 3.48 
                 51.9 
                 19.3 
                 −32.0 
                 346.6 
                 396.6 
                 19.9 
               
               
                 19.0 
                 20.7 
                 293.85 
                 0.0841 
                 0.830 
                 3.48 
                 53.1 
                 20.2 
                 −32.4 
                 384.6 
                 434.6 
                 20.7 
               
               
                 20.0 
                 21.5 
                 294.65 
                 0.0842 
                 0.832 
                 3.47 
                 54.2 
                 21.2 
                 −32.7 
                 424.3 
                 474.3 
                 21.5 
               
               
                 21.0 
                 22.3 
                 295.45 
                 0.0843 
                 0.835 
                 3.47 
                 55.1 
                 22.2 
                 −32.8 
                 465.9 
                 515.9 
                 22.3 
               
               
                 22.0 
                 23.2 
                 296.35 
                 0.0844 
                 0.838 
                 3.47 
                 55.9 
                 23.2 
                 −32.7 
                 509.4 
                 559.4 
                 23.2 
               
               
                 23.0 
                 24.1 
                 297.25 
                 0.0845 
                 0.841 
                 3.46 
                 56.5 
                 24.1 
                 −32.4 
                 554.6 
                 604.6 
                 24.1 
               
               
                 24.0 
                 25.0 
                 298.15 
                 0.0846 
                 0.844 
                 3.46 
                 56.9 
                 25.1 
                 −31.9 
                 601.6 
                 651.6 
                 25.0 
               
               
                 25.0 
                 26.0 
                 299.15 
                 0.0848 
                 0.847 
                 3.46 
                 57.2 
                 26.0 
                 −31.2 
                 650.6 
                 700.6 
                 26.0 
               
               
                 26.0 
                 27.0 
                 300.15 
                 0.0849 
                 0.851 
                 3.46 
                 57.3 
                 27.0 
                 −30.3 
                 701.4 
                 751.4 
                 27.0 
               
               
                 27.0 
                 28.1 
                 301.25 
                 0.0850 
                 0.854 
                 3.46 
                 57.3 
                 27.9 
                 −29.2 
                 754.4 
                 804.4 
                 28.1 
               
               
                 28.0 
                 29.2 
                 302.35 
                 0.0851 
                 0.859 
                 3.46 
                 57.1 
                 28.9 
                 −27.9 
                 809.2 
                 859.2 
                 29.2 
               
               
                 29.0 
                 30.3 
                 303.45 
                 0.0852 
                 0.863 
                 3.46 
                 56.8 
                 29.9 
                 −26.5 
                 865.9 
                 915.9 
                 30.3 
               
               
                 30.0 
                 31.5 
                 304.65 
                 0.0853 
                 0.868 
                 3.47 
                 56.3 
                 30.8 
                 −24.8 
                 924.9 
                 974.9 
                 31.5 
               
               
                   
               
             
          
         
       
     
         [0096]      FIG. 13  shows the values obtained from the simulation with the corresponding compensation curves. It can be seen that the calculated values match the real values very well. Thus, the temperature measured for a short time of the cooling plate in Example 1 at 25 A was −35° C., and the minimum of the compensation curve is approximately −34° C., with a current strength of approximately 21 A and a power of approximately 460 W. And the temperature continuously measured in Example 1 at a power strength of 20 A was −31° C., while the simulation gave 32.8° C. It should be mentioned that the water temperature in the practical experiment varied between 10 and 12° C., while the calculation was based on a constant temperature of 12° C. 
       Examples 3 and 4 
     Two-Stage Device 
       [0097]    Similar to Example 2, a computer simulation for an inventive device as shown in  FIGS. 6 to 8 , i.e. with three Peltier elements arranged side by side or one above the other, was conducted. 
       Example 3 
       [0098]    The calculation of this two-stage embodiment basically followed the one-stage device. First, the current strengths of the primary and secondary stages, i.e. the two lower Peltier elements  2  and  3  or the upper Peltier element  4 , were set as equal, and two data sets, as listed in Example 2 above, were calculated based on the assumption that the water temperature was 12° C. Here, the cold side temperature of the lower stage corresponded to the warm side temperature of the upper stage. 
         [0099]      FIG. 14  shows the values obtained from the simulation with the corresponding compensation curves. In this case, the minimum of the compensation curve was approximately −67° C. with a current strength of 14 to 15 A and a power of approximately 650 W. 
       Example 4 
       [0100]    Subsequently, the calculation was further optimized by calculating a complete data set, as listed above in Example 2, at each current strength in the primary (lower) Peltier stage for the second (upper) stage, wherein the water temperature was assumed to be 10° C. Due to the large data volume, the simulated results are shown only graphically. 
         [0101]      FIG. 15  shows a two-dimensional graph showing the current strengths of the primary and secondary stages on the x or y axis, and the cold side temperature after the second stage, which corresponds to that of the cooling plate of this theoretical two-stage example, i.e. the Tc value of all secondary stages, on the z axis. With a temperature of −72 ° C., a maximum was obtained at a current strength of 17 A for the two Peltier elements of the primary stage and of 11.5 A for the secondary stage. This is marked with an paraxial line in the graph. 
         [0102]    Thus it is clearly shown that the cooling performance of an inventive device using several Peltier elements can be substantially increased compared to the one-stage alternative. A two-stage prototype corresponding to the above simulation is being developed at the moment. If the values that actually measured with this device correspond well to those simulated in Examples 3 and 4, as was the case in Examples 1 and 2, it will prove that a multi-stage device of the invention is a valuable alternative to using dry ice freezing mixtures in low-temperature reactions in laboratories.