A change in the mobile phase strength can be a powerful tool to move peaks in a separation.
Last month's "LC Troubleshooting" concentrated on solvent-type selectivity1 — that is, changing the mobile phase solvent in reversedphase liquid chromatography (LC) separations to change selectivity. Changing solvents is a powerful way to move peaks around in a chromatogram and should not be discounted as a valuable tool for method development. However, you can often get the desired change in selectivity in a simpler way — by changing the solvent strength. When we talk about a strong solvent in reversed-phase separations, we're referring to the organic solvent in the mobile phase — acetonitrile, methanol or tetrahydrofuran in most cases — usually designated as the B-solvent or %B. Thus, a stronger mobile phase would be one with a higher %B. This month we'll look at the regular changes in retention that are observed with a change in the solvent strength and how to take advantage of them when we develop a method.
In many cases with LC separations, it is more useful to deal with the retention factor, k, than with retention time, tR. The retention factor is calculated easily as
where t0 is the column dead time. The dead time can be measured by the injection of an unretained substance, observing the rising baseline at the "solvent front" or estimating the column volume, Vm, for 4.6 mm i.d. columns as
where L is the column length in millimetres. So for a 100 mm × 4.6 mm column, the column volume Vm is ≈ 1 mL. Convert this to t0 by dividing by the flow-rate. At 2 mL/min, we have t0 ≈ 1 mL/2 mL/min ≈ 0.5 min. We'll use this column and flow-rate for the following examples.
In Figure 1 I've shown simulated chromatograms based on a set of data for a group of nitroaromatic compounds on a 100 mm × 4.6 mm, 3 μm dp C18 column operated at a 2 mL/min flowrate. In each case, you can spot the t0 mark at 0.5 min (arrow). We all know from observation that retention time decreases as %B is increased. This is shown with the shorter run times when moving from 55% to 60% to 65% in Figure 1. Another, sometimes overlooked, change is that selectivity or peak spacing, often changes with a change in %B. For example, in Figure 1 at 55%, peaks 2 and 3 are the closest together. We refer to this as the critical peak pair or, if we are interested in resolution, as the minimum resolution. Note that when the mobile phase is changed to 60%, in addition to the shorter run time, the critical peak pair changes to peaks 4 and 5. A further change to 65% additionally shortens the run and also changes the critical peak pair to peaks 3 and 4. When chromatographic conditions are changed and we observe a change in the critical peak pair, the changed variable is one that can be used to control the separation. In the present example, %B can be used to control the separation. This deserves more study.
Figure 1: Simulated chromatograms for a mixture of nitroaromatic compounds using conditions listed in text. Arrow indicates t0.
Notice that each peak in Figure 1 moves in a regular fashion as %B is changed. We can observe this more readily if we calculate k for each peak in each run and plot log k against %B, as shown in Figure 2 for peaks 2–5. Two important observations should be made for Figure 2. First, the lines are, for all practical purposes, linear. This means that they can be described by a simple equation:
where k0 is the k-value at 0% organic, and S is the (negative) slope of the plot. A linear plot means that only two experimental values are needed to calculate k at any %B value. Thus, based on two actual runs, we can predict retention at any other %B value, within the limits of extrapolation from the initial data set, of course.
Figure 2: Plot of log k vs %B for peaks 2, 3, 4, and 5 of Figure 1.
The second observation from Figure 2 is that, although the slope of the lines for the various analytes are roughly the same, there is enough difference in S that peak spacing changes when %B is changed. On the left edge of Figure 2, it is obvious that peaks 2 and 3 are closest together. This was also observed in the 55% plot of Figure 1. Similarly, at the right edge of Figure 2, it is not quite so obvious, but peaks 3 and 4 are closest together, corresponding to the 65% run of Figure 1. The slopes of the lines for peaks 4 and 5 are very similar, so little change in peak spacing is seen with a change in %B. Peak 3, on the other hand, has a different slope from the other peaks and moves relative to peaks 2 and 4 as %B is changed. Visual extrapolation allows us to predict that peaks 2 and 3 will be coeluted at a mobile phase of <55%, whereas peaks 3 and 4 will be coeluted at some mobile phase >65%.
These two observed behaviours — linearity and a change in relative peak spacing with a change in %B — are what makes solvent strength such a powerful tool for method development. It means that we can leverage a small amount of experimental data to predict the separation under other conditions.
To take full advantage of solvent strength, we need to make two more calculations, α and N:
where α is the selectivity or relative peak spacing, for an adjacent pair of peaks with k-values k1 and k2.
where N is the column plate number (column efficiency) and w is the peak width measured at baseline between tangents drawn to the sides of the peak.
We can combine k, α and N to form what is called the fundamental resolution equation:
where Rs is the resolution between two peaks of interest, and k usually refers to the first peak of a peak pair of interest.
Now we have all the information to calculate resolution at any %B for a separation. We first determine the behaviour of each peak by making two experimental runs and obtaining the data necessary to calculate k at any %B using Equation 3. Now we can determine factor (iii) of Equation 6. If we know k for each peak at any %B, then α for each peak pair can be calculated using Equation 4. This gives us data for factor (ii) of Equation 6. All we need to finish the job is to either measure N or for many purposes, an estimate of N is sufficient. A 150 mm column containing 5 μm particles or a 100 mm column filled with 3 μm particles each will generate N ≈ 10000 for real samples. This is a handy number because (10000)0.5 = 100, so now Equation 6 simplifies to
which can be used to estimate resolution for any peak pair at any %B based on data from only two experimental runs.
Although Equations 6 or 7 allow us to calculate resolution for each pair of peaks at various mobile phase strengths, it usually is not the resolution of all peak pairs that we are interested in. We are more interested in the resolution of the critical pair of peaks. If we calculate the resolution between each pair of peaks for a given %B, we can determine which peak pair is the critical peak pair. If we plot the resolution of only the critical peak pair against %B, we get a resolution map, as is shown in the lower part of Figure 3. Chromatograms for peaks 2–5 of Figure 1 are shown for several points on the resolution map (peak intensities slightly different between Figures 1 and 3).
Figure 3: A resolution map for the sample of Figure 1 showing partial chromatograms for peaks 2, 3, 4 and 5. Critical peak pair is circled in each case (peak intensity differs slightly between Figures 1 and 3).
Several powerful aspects of the resolution map should be readily apparent. First, the conditions for the highest resolution are quickly identified: ≈ 56%. To find this optimum with a search-and-refine optimization process would require many more than two or three runs. For example, an initial run at 90% would give extremely short retention times. A change to 70% would give a chromatogram with k ≈ 1 for the first peak and a run time of about 2 min. Then we might begin refining the conditions 5% at a time until we got close — probably 6–8 runs at a minimum. Instead, we could use the second (70%) run as one of the inputs and then drop %B by 10–15% for a 60% or 55% run. With these three runs (one wasted and two useful), we have sufficient data to generate the resolution map. Finding the conditions for the best resolution is well worth two or three runs.
A second aspect of the resolution map is that we can quickly identify conditions to avoid — in particular those where peak coelution occurs. Coelutions happen whenever the resolution map dips to zero resolution, such as at ≈ 40%, ≈ 50% and ≈ 70%. At each of these conditions, one or more peak pairs overlap completely. For example, in the right-hand chromatogram at the top of Figure 3, the middle two peaks are seen to be the critical peak pair (circled); as %B is increased, the peaks will move closer together until they are coeluted at 70%, then their resolution will increase as they reverse order and pull apart.
A third important use of the resolution map is to estimate the robustness of the separation to the variable of interest — %B in this case. We can see that the highest resolution is at ≈ 56%B, but it drops off rapidly as %B is decreased. Nevertheless, resolution decreases less rapidly as %B is increased. The relatively flat region of the map between ≈ 56% and ≈ 65% will lead us to conclude that if we use 60% as the default mobile phase concentration, the method would be able to tolerate ≈ ± 2%B without major loss in resolution. We could use this information to identify limits to test for robustness testing.
In some ways, the resolution map seems almost too good to be true. Can you really make just two runs and predict retention and resolution at any other %B? Well, yes and no. The "rubbish-in-rubbish-out" principle holds here — if you gather high quality input data to make the calculations, the results can be quite good. Predictions of k easily have errors of < 5% for interpolation between the initial runs and with reasonable extrapolation beyond the input values. Predicted values of resolution are likely to be less accurate due to two factors. One of these has to do with the selection of the plate number used in the calculations. Equation 7 assumes N = 10000, and it is obviously limited to these conditions. Equation 6 uses a single plate number for all peaks — a generalization that will compromise the predictions, but not too dramatically if the plate number of the peaks of interest is used. The biggest shortcoming of Equation 6 is that it does not take peak asymmetry into account. Most peaks tail to some extent, and this tailing tends to reduce resolution. Corrections for tailing are too involved for this limited discussion, but commercial resolution mapping software, such as DryLab (Molnar Institut, Berlin, Germany) can take peak tailing and plate numbers for each peak into account when generating a resolution map, for more accurate results. In any event, the resolution map generated from Equations 6 or 7 will identify the conditions for the largest resolution, even if the predicted value of resolution is not exactly what is observed experimentally.
Last month's "LC Troubleshooting"1 looked at the use of solvent-type selectivity as a means to control the peak spacing in a chromatogram. This month we've looked at the alternative of solvent-strength selectivity.
Although solvent-strength changes typically show less-dramatic effects on selectivity than changes in solvent type do, solvent-strength selectivity is powerful enough to identify satisfactory separation conditions in many cases. Because this technique requires only two or three experimental runs, it is easier and faster than changing from one solvent to another. And if %B adjustments alone are insufficient to obtain the desired separation, you have identified conditions for one of the corners of the solventselectivity triangle approach discussed last month. For these reasons, I recommend exploring solvent strength before solvent type during method development. Although you can perform all the calculations manually using the equations given here, the process will be much faster and less frustrating if you use commercial resolution modelling software.
"LC Troubleshooting" editor John Dolan is vice president of LC Resources, Walnut Creek, California, USA. He is also a member of LCGC Europe's editorial advisory board. Direct correspondence about this column to LCGC Europe editor, Alasdair Matheson, at firstname.lastname@example.org
1. J.W. Dolan, LCGC Eur., 23(12), 581–584 (2010).
Mabadiliko katika nguvu ya awamu ya kusafiri inaweza kuwa chombo nguvu ya kuhamisha vilele katika kutenganisha. "Lichapisha ""Licensing"" ya mwezi uliopita, ambayo inazingatia aina ya selectivity ya solvent, yaani, kubadilisha solvent ya awamu ya simu katika kutenganisha kwa kromatografia ya kioevu ya awamu ya nyuma (LC) ili kubadilisha selectivity." Kubadilisha solvents ni njia yenye nguvu ya kuhamisha vilele karibu katika chromatogram na haipaswi kupunguzwa kama chombo muhimu kwa ajili ya maendeleo ya mbinu. Hata hivyo, unaweza mara nyingi kupata mabadiliko yaliyotakiwa katika uteuzi kwa njia rahisi <unk> kwa kubadilisha nguvu ya mchanganyiko. Wakati sisi kuzungumza juu ya solvent nguvu katika kugeuka awamu ya kutenganisha, sisi ni akimaanisha solvent kikaboni katika awamu ya simu - acetonitrile, methanol au tetrahydrofuran katika kesi nyingi - kawaida maalum kama B-solvent au% B. Hivyo, awamu ya nguvu ya simu itakuwa moja na juu ya %B. Katika kipindi hiki tutaangalia mabadiliko ya kawaida katika uhifadhi ambayo huonekana na mabadiliko katika nguvu ya mchanganyiko na jinsi ya kuitumia wakati tunatengeneza mbinu. Katika kesi nyingi na LC kutenganisha, ni muhimu zaidi kushughulika na uhifadhi sababu, k, kuliko na uhifadhi muda, tR. Uhifadhi Factor ni kuhesabiwa kwa urahisi kama ambapo t0 ni safu ya muda wa wafu. Wakati wa kufa unaweza kupimwa kwa sindano ya dutu unretentioned, kuchunguza kuongezeka kwa msingi katika "solvent mbele" au kukadiria wingi wa safu, Vm, kwa ajili ya 4.6 mm id. Koloni L ni urefu wa safu katika milimita. Kwa mfano, kwa safu ya 100mm × 4.6mm, kiasi cha safu ya Vm ni <1ml. Kubadilisha hii kwa t0 kwa kugawanya na mtiririko-kiwango. Kwa m2m, t = 1 mL = 2 mL = 0.5 min. Tutatumia safu hii na mtiririko-kiwango kwa ajili ya mifano ifuatayo. Katika picha ya 1 nimeonyesha chromatograms simulated kulingana na seti ya data kwa ajili ya kundi la nitroaromatic misombo juu ya 100 mm × 4.6 mm, 3 μm dP-C18 safu kuendeshwa katika 2 mL min mtiririko. Katika kila kesi, unaweza kuona alama ya t0 katika dakika 0.5 (mishale). Sisi sote tunajua kutoka kwa uchunguzi kwamba muda wa kuhifadhi hupungua kama% B inaongezeka. Hii inaonyeshwa na muda mfupi wa kukimbia wakati wa kuhamia kutoka 55% hadi 60% katika Picha 1. Nyakati nyingine, wakati mwingine overlooked, mabadiliko ni kwamba uteuzi au kilele spacing, mara nyingi mabadiliko na mabadiliko katika %B. Kwa mfano, katika picha ya 1 na 55%, kilele 2 na 3 ni karibu zaidi pamoja. Sisi rejea hii kama muhimu kilele jozi au, kama sisi ni nia ya azimio, kama azimio chini. Wakati hatua ya kuhamisha ni kubadilishwa kwa 60%, pamoja na muda mfupi wa kukimbia, jozi muhimu ya kilele hubadilika kwa kilele 4 na 5. Mabadiliko ya juu ya 65% pia hupunguza kukimbia na pia hubadilisha jozi muhimu ya kilele kwa kilele 3 na 4. Wakati hali chromatographic ni kubadilishwa na sisi kuchunguza mabadiliko katika muhimu kilele jozi, kubadilika variable ni moja ambayo inaweza kutumika kudhibiti kutenganisha. Katika mfano huu, %B inaweza kutumika kudhibiti kutenganisha. Jambo hilo linastahili kuchunguzwa zaidi. Chapa ya kwanza: Chromatograms ya simulated kwa mchanganyiko wa nitroaromatic compounds kwa kutumia hali zilizoorodheshwa katika maandishi. Mshale unaonyesha t0. Kwa mfano, kila kilele cha picha 1 kinabadilika kwa njia ya kawaida wakati %B inabadilishwa. Hii inaweza kuonekana kwa urahisi zaidi ikiwa tunahesabu k kwa kila kilele katika kila kukimbia na kuchora log k dhidi ya %B, kama inavyoonyeshwa katika Picha 2 kwa kilele 2 < 5. Maelezo mawili muhimu yanapaswa kufanywa kwa Mchoro wa 2. Kwanza, mistari hiyo ni ya mstari-mstari. Hii ina maana kwamba wanaweza kuelezwa na equation rahisi: ambapo k0 ni k-thamani katika 0% kikaboni, na S ni (negative) mteremko wa plot. Plot linear ina maana kwamba tu mbili majaribio maadili zinahitajika kuhesabu k katika thamani yoyote %B. Kwa hivyo, kulingana na mbio mbili halisi, tunaweza kutabiri uhifadhi kwa thamani nyingine yoyote ya %B, ndani ya mipaka ya extrapolation kutoka kwa seti ya data ya awali, bila shaka. Picha ya pili: Picha ya log k vs %B kwa kilele 2, 3, 4 na 5 ya Picha ya 1. Utafiti wa pili kutoka kwa Mchoro wa 2 ni kwamba, ingawa mteremko wa mistari kwa ajili ya analytes mbalimbali ni sawa, kuna tofauti ya kutosha katika S kwamba upeo wa nafasi hubadilika wakati %B inabadilishwa. Katika sehemu ya kushoto ya picha ya pili, kuna mviringo wa pili na wa tatu. Hii pia ilionekana katika mchoro wa 55% wa Mchoro 1. Kwa upande wa kulia wa picha ya pili, pigo la 3 na 4 ni karibu zaidi, ikilinganishwa na asilimia 65 ya picha ya kwanza. Mteremko wa mstari wa 4 na 5 ni sawa sana, kwa hivyo mabadiliko machache katika nafasi ya kilele huonekana na mabadiliko ya %B. Piki ya 3 ina mwinuko tofauti na piki nyingine na inahama ikilinganishwa na piki ya 2 na 4 wakati %B inabadilika. Kwa mfano, kwa mfano, kwa mfano, kwa mfano, kwa mfano, kwa mfano, kwa mfano, kwa mfano, kwa mfano, kwa mfano, kwa mfano, kwa mfano, kwa mfano, kwa mfano, kwa mfano, kwa mfano, kwa mfano, kwa mfano, kwa mfano. Hizi mbili kuonekana tabia <unk> linearity na mabadiliko katika jamaa kilele spacing na mabadiliko katika %B <unk> ni nini hufanya nguvu ya solvent kama chombo nguvu kwa ajili ya maendeleo ya mbinu. Hii inamaanisha kwamba tunaweza kutumia kiasi kidogo cha data ya majaribio kutabiri mgawanyiko chini ya hali nyingine. Ili kuweza kuondoa athari za kioevu, ni muhimu kufanya hesabu mbili za kioevu: k2 na k3, ambapo k2 ni kioevu cha k2 na k3 ni kioevu cha k3. ambapo N ni safu ya safu ya safu (ufanisi wa safu) na w ni upana wa kilele kilichopimwa kwenye mstari wa msingi kati ya tangents iliyochorwa kwa pande za kilele. "Kuna ""k"" na ""n"" ambazo zinaunganishwa na kuunda ""mfano wa msingi wa azimio"" ambapo ""r"" ni azimio kati ya vilele viwili vya maslahi, na ""k"" kwa kawaida inahusu kilele cha kwanza cha jozi ya kilele cha maslahi." Sasa tuna habari zote kwa mahesabu azimio katika yoyote %B kwa ajili ya kutenganisha. Kwa mfano, kwa mfano, kwa mfano, kwa mfano, kwa mfano, kwa mfano, kwa mfano, kwa mfano, kwa mfano, kwa mfano, kwa mfano, kwa mfano, kwa mfano, kwa mfano, kwa mfano, kwa mfano, kwa mfano, kwa mfano, kwa mfano, kwa mfano. Sasa tunaweza kuamua sababu (iii) ya equation 6. Kama tunajua k kwa kila kilele katika yoyote %B, basi α kwa kila jozi kilele inaweza kuhesabiwa kwa kutumia equation 4. Hii inatoa data kwa sababu (ii) ya equation 6. Yote tunahitaji kumaliza kazi ni ama kupima N au kwa madhumuni mengi, makadirio ya N ni ya kutosha. Kwa mfano, safu ya 150mm iliyo na chembe za 5mm au safu ya 100mm iliyojazwa chembe za 3mm kila moja itazalisha N = 10000 kwa sampuli halisi. Hii ni namba rahisi kwa sababu (10000) 0.5 = 100, hivyo sasa Equation 6 kurahisisha ambayo inaweza kutumika kukadiria azimio kwa jozi yoyote kilele katika % B yoyote kulingana na data kutoka mbio mbili tu majaribio. Ingawa Equation 6 na 7 zinatuwezesha kuhesabu azimio kwa kila jozi ya kilele katika nguvu mbalimbali za awamu ya kusafiri, kwa kawaida si azimio la jozi zote za kilele ambazo tunapendezwa nazo. Sisi ni zaidi ya nia ya azimio la jozi muhimu ya vilele. Ikiwa tunahesabu azimio kati ya kila jozi ya kilele kwa %B iliyopewa, tunaweza kuamua ni jozi gani ya kilele ni jozi muhimu ya kilele. Kwa mfano, ikiwa tunapiga picha ya azimio la pete ya pigo muhimu dhidi ya %B, tunapata ramani ya azimio, kama inavyoonyeshwa katika sehemu ya chini ya Picha 3. Chromatograms kwa ajili ya kilele 2 na 5 ya Picha 1 ni kuonyeshwa kwa pointi kadhaa juu ya ramani azimio (kiwango cha kilele tofauti kidogo kati ya Picha 1 na 3). Picha ya 1 - Picha ya 1 ya mchoro wa chromatogram ya sehemu ya pigo 2, 3, 4 na 5. Piki ya kipekee ya pini ya pini ya pini ya pini ya pini ya pini ya pini ya pini ya pini ya pini ya pini ya pini ya pini ya pini ya pini ya pini ya pini ya pini ya pini ya pini ya pini ya pini ya pini ya pini. Mambo kadhaa yenye nguvu ya ramani ya azimio inapaswa kuwa wazi kwa urahisi. Kwanza, hali kwa ajili ya azimio la juu ni haraka kutambuliwa: < 56%. Kupata hii bora na mchakato wa utafutaji-na-kufupisha optimization ingehitaji mengi zaidi ya mbio mbili au tatu. Kwa mfano, mbio ya awali ya 90% itatoa muda mfupi sana wa kuhifadhi. Kwa mfano, kwa kiwango cha 70% chromatogram ya k < 1 kwa kilele cha kwanza na wakati wa kukimbia wa dakika 2. Kwa hivyo, tunaweza kuanza kuboresha hali kwa 5% kwa wakati mmoja hadi tutakapokaribia <unk> labda 6<unk>8 inaendesha angalau. Kwa mfano, unaweza kutumia mbio ya pili (70%) kama moja ya pembejeo na kisha kupunguza %B kwa 10-15% kwa mbio ya 60% au 55%. Pamoja na mbio hizi tatu (moja wasted na mbili muhimu), tuna data ya kutosha kuzalisha ramani azimio. Kupata hali kwa ajili ya azimio bora ni vizuri thamani ya mbio mbili au tatu. Kipengele cha pili cha ramani ya azimio ni kwamba tunaweza haraka kutambua hali ya kuepuka <unk> hasa wale ambapo kilele coelution hutokea. Coelution ni hali ambayo hutokea wakati wowote ambapo map ya azimio hupungua hadi azimio la sifuri, kama vile <40%, <50% na <70%. Katika kila moja ya hali hizi, moja au zaidi pairs kilele overlap kabisa. Kwa mfano, katika chromatogram ya kulia juu ya Picha 3, kilele mbili za kati zinaonekana kuwa jozi muhimu ya kilele (kuzunguka); kama% B inaongezeka, kilele kitaendelea kukaribia pamoja hadi zitakapokuwa na coelutation ya 70% na kisha azimio lao litakua wakati wao wanageuka na kujitenga. Tatu muhimu matumizi ya ramani azimio ni kukadiria nguvu ya kutenganisha kwa variable ya maslahi <unk>%B katika kesi hii. Kwa mfano, kwa mfano, kiwango cha juu cha azimio ni <56%, lakini inashuka kwa kasi wakati <50% inashuka. Hata hivyo, azimio hupungua chini kwa kasi kama% B ni kuongezeka. Sehemu ya mviringo ya ramani kati ya <50% na <65% itatuongoza kuhitimisha kwamba ikiwa tutatumia 60% kama mkusanyiko wa awamu ya mwendo wa kawaida, njia hiyo ingeweza kuvumilia <2%B bila kupoteza kubwa katika azimio. Tunaweza kutumia taarifa hii kutambua mipaka ya mtihani kwa ajili ya mtihani robustness. Kwa njia fulani, ramani ya azimio inaonekana kuwa nzuri sana kuwa kweli. Je, unaweza kweli kufanya tu mbio mbili na kutabiri uhifadhi na azimio katika yoyote nyingine %B? Naam, na la. "Rubbish-katika-rubbish-nje" kanuni inashikilia hapa <unk> kama wewe kukusanya data ya juu ya ubora wa pembejeo kufanya mahesabu, matokeo inaweza kuwa nzuri sana. Utabiri wa k kwa urahisi kuwa na makosa ya <5% kwa interpolation kati ya mbio za awali na na extrapolation busara zaidi ya maadili ya pembejeo. Thamani zilizotabiriwa za azimio zinaweza kuwa na usahihi mdogo kwa sababu mbili. Mojawapo ya mambo hayo inahusiana na uteuzi wa nambari ya chapa inayotumiwa katika mahesabu. Kwa mfano, equation 7 inadhani N = 10000, na ni wazi kwamba ni mdogo kwa masharti haya. Mlinganisho wa 6 hutumia namba moja ya sahani kwa kilele vyote - jumla ambayo itahatarisha utabiri, lakini sio sana ikiwa idadi ya sahani ya kilele cha maslahi hutumiwa. Kosa kubwa la equation 6 ni kwamba haina kuchukua kilele asymmetry katika akaunti. Vipimo vingi hufuata kwa kiasi fulani, na kufuata huko huelekea kupunguza azimio. "Kupitia programu ya ""DryLab"" (Molnar Institute, Berlin, Ujerumani) unaweza kuchukua pike tailing na idadi ya sahani kwa kila kilele katika akaunti wakati wa kuzalisha ramani ya azimio, kwa matokeo sahihi zaidi." Kwa hali yoyote, ramani ya azimio iliyotengenezwa kutoka kwa equation 6 au 7 itatambua hali za azimio kubwa zaidi, hata kama thamani ya azimio iliyotarajiwa sio kile kinachotambuliwa kwa majaribio. "Leo, katika ""Lighting Up"" tulijadili jinsi ya kuondoa rangi ya rangi ya rangi ya rangi ya rangi ya rangi ya rangi ya rangi." Mwezi huu tumeangalia mbadala wa selectivity nguvu ya mchanganyiko. Ingawa mabadiliko ya nguvu ya solvent kwa kawaida huonyesha athari ndogo ya kuvutia juu ya uteuzi kuliko mabadiliko katika aina ya solvent, uteuzi wa nguvu ya solvent ni nguvu ya kutosha kutambua hali ya kutenganisha ya kuridhisha katika kesi nyingi. Kwa sababu mbinu hii inahitaji majaribio mawili au matatu tu, ni rahisi na ya haraka kuliko kubadilisha kutoka kwa mchanganyiko mmoja hadi mwingine. Kama %B marekebisho peke yake ni haitoshi kupata kutenganisha taka, umebainisha hali kwa ajili ya moja ya pembe ya solvent selectivity pembetatu mbinu kujadiliwa mwezi uliopita. Kwa sababu hizi, mimi kupendekeza kuchunguza nguvu ya solvent kabla ya aina ya solvent wakati wa maendeleo ya mbinu. Ingawa unaweza kufanya mahesabu yote manually kutumia equations alitoa hapa, mchakato itakuwa haraka sana na chini ya kukatisha tamaa kama wewe kutumia kibiashara azimio modeling programu. "LLC Troubleshooting" mhariri John Dolan ni makamu wa rais wa LC Resources, Walnut Creek, California, USA. Yeye pia ni mwanachama wa LCGC Ulaya ya uhariri bodi ya ushauri. Kwa mujibu wa taarifa ya gazeti la The Guardian, mkurugenzi wa LCGC Ulaya, Alasdair Matheson, aliandika barua pepe kwa jina la kwanza, jina la mwisho, na mfano. J. W. "Dolan, LCGC Eur., 23 (12) 581-584 (2010). """""