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Response factor
Response factor
Response factor
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Response factor, usually in chromatography and spectroscopy, is the ratio between a signal produced by an analyte, and the quantity of analyte which produces the signal. Ideally, and for easy computation, this ratio is unity (one). In real-world scenarios, this is often not the case.

Expression

[edit]

The response factor can be expressed on a molar, volume or mass[1] basis. Where the true amount of sample and standard are equal:

where A is the signal (e.g. peak area) and the subscript i indicates the sample and the subscript st indicates the standard.[2] The response factor of the standard is assigned an arbitrary factor, for example 1 or 100. Response factor of sample/Response factor of standard=RRF

Chromatography

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One of the main reasons to use response factors is to compensate for the irreproducibility of manual injections into a gas chromatograph (GC). Injection volumes for GCs can be 1 microliter (μL) or less and are difficult to reproduce. Differences in the volume of injected analyte leads to differences in the areas of the peaks in the chromatogram and any quantitative results are suspect.

To compensate for this error, a known amount of an internal standard (a second compound that does not interfere with the analysis of the primary analyte) is added to all solutions (standards and unknowns). This way if the injection volumes (and hence the peak areas) differ slightly, the ratio of the areas of the analyte and the internal standard will remain constant from one run to the next.

This comparison of runs also applies to solutions with different concentrations of the analyte. The area of the internal standard becomes the value to which all other areas are referenced. Below is the mathematical derivation and application of this method.

Consider an analysis of octane (C8H18) using nonane (C9H20) as the internal standard. The 3 chromatograms below are for 3 different samples.

The amount of octane in each sample is different, but the amount of nonane is the same (in practice this is not a requirement). Due to scaling, the areas of the nonane peak appear to have different areas, but in reality the areas are identical. Therefore, the relative amounts of octane in each sample increases in the order of mixture 1 (least) < mixture 3 < mixture 2 (most).

This conclusion is reached because the ratio of the area of octane to that of nonane is the least in mixture 1 and the most, in mixture 2. Mixture 3 has an intermediate ratio. This ratio can be written as .

In chromatography, the area of a peak is proportional to the number of moles (n) times some constant of proportionality (k), Area = k×n. The number of moles of compound is equal to the concentration (molarity, M) times the volume, n = MV. From these equations, the following derivation is made:

Since both compounds are in the same solution and are injected together, the volume terms are equal and cancel out. The above equation is then rearranged to solve for the ratio of the k's. This ratio is then called the response factor, F.

The response factor, F, is equal to the ratios of the k's, which are constant. Therefore, F is constant. What this means is that regardless of the amounts of octane and nonane in solution, the ratio of the ratios of area to concentration will always yield a constant.

In practice, a solution containing known amounts of both octane and nonane is injected into a GC and a response factor, F, is calculated. Then a separate solution with an unknown amount of octane and a known amount of nonane is injected. The response factor is applied to the data from the second solution and the unknown concentration of the octane is found.

This example deals with the analysis of octane and nonane, but can be applied to any two compounds.

References

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Response factor

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from Grokipedia
In , the response factor is a fundamental that measures the detector's sensitivity to a specific , defined as the ratio of the instrument's signal output—typically the peak area in chromatographic techniques—to the analyte's concentration or amount. It plays a crucial role in quantitative analysis across methods such as (GC) and (HPLC), enabling the conversion of detector responses into accurate concentration values for compounds in complex samples. Response factors are calculated experimentally by injecting standards of known concentrations and determining the ratio of peak area to concentration, often represented as the slope of a calibration curve plotting response against concentration. In many applications, relative response factors (RRFs) are employed instead, defined as the ratio of an analyte's response factor to that of a reference standard (such as the active pharmaceutical ingredient in drug analysis), which allows for reliable quantification of impurities or related substances even without their pure standards. This relative approach is particularly valuable in pharmaceutical and environmental testing, where it improves accuracy by accounting for variations in detector response due to molecular structure, volatility, or polarity differences among analytes. The use of response factors is integral to , as outlined in methods like EPA Method 8270E for semivolatile organics by GC/, where minimum response factors must be met to ensure system performance before sample analysis. Factors influencing response factors include detector type (e.g., flame ionization or ), instrumental conditions, and properties, often requiring internal standards—chemically similar compounds added to samples—for robust and to minimize errors from matrix effects or injection variability. Overall, response factors enhance the precision and of trace-level determinations in fields ranging from to .

Fundamentals

Definition

In , particularly in techniques such as and , the response factor is defined as the ratio of the detector signal—typically the peak area or height—generated by an to the quantity of that analyte, such as its concentration or mass. This measure captures the inherent sensitivity of a detection system to a specific compound, enabling the translation of instrumental output into quantitative information. The primary role of the response factor lies in compensating for variations in detector sensitivity among different analytes, which arise due to differences in molecular structure, volatility, or ionization efficiency. By applying this factor, analysts can achieve accurate quantification of components in complex mixtures without requiring individual calibration for every compound, thereby streamlining quantitative analysis in fields like pharmaceutical testing and environmental monitoring. The concept of the response factor emerged in the mid-20th century, coinciding with the development of and associated detectors, including the (FID) introduced in the 1950s for analysis. This period marked a shift toward reliable quantitative separations, where response factors became essential for interpreting detector signals in early chromatographic workflows. In contrast to comprehensive calibration curves, which plot detector signal against analyte concentration to accommodate potential non-linearity or baseline offsets, the response factor method simplifies procedures by assuming a linear detector response passing through the origin, thus representing the slope of that idealized line. This assumption facilitates rapid calculations but requires validation of linearity for reliable use.

Mathematical Formulation

The (RF) in , particularly in , is mathematically defined as the ratio of the detector signal produced by an to its concentration, providing a quantitative measure of detector sensitivity. The basic equation is expressed as: RF=SC\text{RF} = \frac{S}{C} where SS represents the signal intensity, often the peak area AA in chromatographic analysis, and CC is the concentration. In practice, for external standard , this simplifies to RF=AC\text{RF} = \frac{A}{C}, assuming the signal is proportional to the amount injected. For the internal standard method, which enhances accuracy by compensating for variations in injection volume or detector response, the relative response factor (RRF) is derived relative to a known standard. The is: RRF=(Aanalyte/Canalyte)(Astandard/Cstandard)\text{RRF} = \frac{(A_\text{analyte} / C_\text{analyte})}{(A_\text{standard} / C_\text{standard})} This ratio isolates the 's intrinsic response by normalizing against the standard's signal and concentration. The derivation assumes that both and standard experience identical analytical conditions, yielding a constant RRF value independent of absolute amounts. The validity of these equations relies on the assumption of in the detector response, where RF remains constant across a specified concentration range because the signal-concentration relationship follows a straight line passing through the origin. Deviations from , such as at high concentrations due to saturation, invalidate this constancy and require range-specific RF values. Regarding units, RF is typically dimensionless when signal and concentration are expressed in consistent units (e.g., arbitrary area units per arbitrary concentration units), but it may carry specific dimensions like area per concentration, such as mV·min/μg for UV absorbance detectors in (HPLC). As an illustrative example, consider an yielding a peak area of 100 arbitrary units at a concentration of 1 μg/mL; the RF is then calculated as RF=100/1=100\text{RF} = 100 / 1 = 100 (arbitrary units per μg/mL).

Applications

In Chromatography

In (GC), response factors play a crucial role in compensating for irreproducibility associated with manual sample injection, where variations in injected volume can introduce significant errors in quantification. By employing an method, the response factor—calculated as the ratio of the analyte's detector response to its concentration relative to the internal standard—normalizes these injection variabilities, ensuring more accurate and reproducible results across multiple runs. This approach is particularly valuable in GC analyses of volatile compounds, as it mitigates inconsistencies in sample introduction without requiring autosamplers. In (HPLC), response factors are essential for impurity profiling in pharmaceutical formulations, enabling the quantification of minor components relative to the primary . These factors account for differences in detector sensitivity between the main substance and its impurities, allowing for precise determination of trace-level contaminants even when their concentrations are low. For instance, in the analysis of active pharmaceutical ingredients, response factors facilitate the estimation of impurities by comparing their peak areas to those of the reference standard under identical conditions. Response factors integrate seamlessly with common detectors in these techniques. In GC, the flame ionization detector (FID) generates a signal proportional to the number of carbon atoms in the , providing a nearly universal response for organic compounds that informs the response factor calculation. In HPLC, (UV) absorbance detectors rely on the strength of the analyte's —the responsible for light absorption—determining the response factor based on molar absorptivity at the selected . A practical example in pharmaceutical involves using response factors to report impurities below the calibration range, assuming detector over the extended low-concentration region. This method allows estimation of impurity levels as low as 0.05% without dedicated standards for each minor component, supporting compliance with regulatory thresholds. The advantages of this approach include reducing the need for multiple reference standards, which streamlines method development and validation while aligning with guidelines such as ICH Q3A for impurity control in drug substances.

In Spectroscopy and Mass Spectrometry

In ultraviolet-visible (UV-Vis) spectroscopy, the response factor establishes the proportional relationship between analyte absorbance and concentration, adapting Beer's Law to accommodate differences in molar absorptivity among compounds. Beer's Law is expressed as A=ϵlcA = \epsilon l c, where AA is absorbance, ϵ\epsilon represents the molar absorptivity (functioning as the core response factor), ll is the optical path length, and cc is the analyte concentration; this formulation enables precise quantitation by calibrating against standards with characterized response factors, particularly in multicomponent mixtures where overlapping spectra necessitate derivative techniques for resolution. In (MS), the response factor primarily denotes the efficiency of analytes, with (ESI) exemplifying how polarity influences signal generation, as more polar compounds exhibit higher ionization yields due to better charge retention in the droplet fission process. The historical advancement of ESI-MS in the late and , pioneered by John Fenn's work on interfacing liquid samples to MS, highlighted the need for response factors to address variable ionization efficiencies, transforming the technique into a cornerstone for analyzing polar biomolecules and pharmaceuticals where traditional methods failed. Hyphenated techniques like liquid chromatography-mass spectrometry (LC-MS) and gas chromatography-mass spectrometry (GC-MS) leverage response factors to compensate for matrix effects and suppression, which can alter signals in complex samples by competing for ionization sites in the source. In LC-ESI-MS, for example, matrix components may suppress up to 50-90% of analyte response through , prompting the use of relative response factors derived from isotopically labeled internal standards to normalize data and enhance accuracy across diverse matrices. These response factors find critical applications in environmental analysis, such as PAH quantitation in ambient air extracts via GC-MS, where relative response factors to deuterated surrogates correct for detector nonlinearities and ensure compliance with regulatory limits like those in EPA Method TO-13A. In pharmaceutical extractables and leachables (E&L) testing, LC-MS response factors mitigate variability in detecting packaging-derived impurities, with multi-detector approaches reducing relative response factor spreads from over 100-fold to under 10-fold, thereby lowering uncertainty in safety assessments. A key challenge in MS-based methods is the non-linear response arising from ion suppression, where co-ionizing species diminish signal at higher concentrations, deviating from ideal proportionality and necessitating response factor recalibration or dilution strategies to restore over dynamic ranges spanning three to five orders of magnitude.

Determination Methods

Experimental Determination

The experimental determination of absolute response factors (RFs) primarily involves direct calibration, where standard solutions of the at known concentrations are prepared and analyzed under controlled conditions. These solutions are injected into the chromatographic system, typically in multiple replicates (n=3–6) to account for variability, and the RF is calculated as the average ratio of the detector signal (e.g., peak area) to the analyte concentration, as detailed in the mathematical formulation section. An alternative approach is the internal standard method, which employs a compound with a known absolute RF added to the standards at a fixed concentration. The RF is then derived from the ratio of the response to the response, multiplied by the reference's known RF, enabling correction for injection volume fluctuations and instrument drift while maintaining absolute quantification. For (GC), flame ionization detection (FID) is commonly used due to its near-universal response to organic compounds, while (HPLC) typically employs ultraviolet (UV) or (MS) detectors for selective response measurement. Validation of the determined RFs is essential to ensure reliability, assessing across the analytical range with a (R²) greater than 0.99, precision via relative standard deviation (RSD) below 5% for replicate injections, and the operational range covering expected levels; these evaluations should be performed on the day of to confirm stability. In regulatory contexts, such as pharmacopeial methods, absolute RF determination is required for accurate impurity quantification, aligning with guidelines like USP <1225> that emphasize validated calibration to support method accuracy in pharmaceutical analysis.

Relative Response Factors

Relative response factors (RRFs) serve as a comparative metric in analytical chemistry, particularly for quantifying impurities or related compounds relative to a primary reference standard. The RRF is defined as the ratio of the response factor (RF) of the target analyte (often an impurity) to the RF of the reference compound, which is typically the active pharmaceutical ingredient (API) in drug analysis. This approach assumes that the detector response is proportional to concentration, enabling efficient impurity profiling without dedicated standards for every component. RRFs are commonly calculated from the slopes of calibration curves obtained under identical chromatographic conditions. Specifically, the RRF is determined as: RRF=slope of calibration curve for impurityslope of calibration curve for reference\text{RRF} = \frac{\text{slope of calibration curve for impurity}}{\text{slope of calibration curve for reference}} This method leverages from standard solutions, where the slope represents the sensitivity (response per unit concentration) for each compound. For validation, the RRF should ideally fall within 0.8–1.2 to avoid correction factors, as outlined in ICH Q2(R2) guidelines for analytical procedures. In pharmaceutical applications, RRFs are integral to impurity testing under ICH Q3B(R2) guidelines, allowing degradation products in drug products to be quantified relative to the when responses are comparable, thereby streamlining method development for stability studies. Similarly, in , RRFs facilitate the analysis of like alkylated polycyclic aromatic hydrocarbons (PAHs), where impurities or congeners are measured against parent PAHs to assess levels in complex matrices such as sediments or air particulates. The primary advantage of RRFs lies in minimizing requirements, as they exploit structural similarities between the and to approximate responses, reducing analytical overhead while maintaining accuracy for trace-level detection. For example, if the RF of an is 1.0 and an impurity's RF is 0.5 under UV detection at 254 nm, the RRF equals 0.5; thus, for equal concentrations, the impurity's peak area would be half that of the , requiring multiplication of the observed area by the RRF to estimate true impurity levels. Recent post-2020 studies emphasize modeling in RRF applications, incorporating day-of-analysis recalibration and factors (e.g., ±20% for stability-indicating assays) to propagate errors from instrument drift or matrix effects. This quantitative adjustment ensures reliable reporting thresholds in regulated analyses.

Influencing Factors

Detector and Instrument Variations

The response of detectors to analytes in chromatographic and spectrometric techniques fundamentally influences the consistency of response factors (RFs). In (GC) with ionization detection (FID), the detector generates a signal proportional to the number of carbon-hydrogen (C-H) bonds in the , as organic compounds are combusted in a to produce . This response is quantified using the effective carbon number (ECN) theory, which generally equals the number of carbon atoms for hydrocarbons, with adjustments (typically subtractions) for functional groups to predict relative RFs without individual calibration. In (HPLC) with (UV) detection, RFs depend on the 's at its maximum (λ_max), typically in the 200–400 nm range, where conjugated systems or chromophores enhance sensitivity. For (MS), particularly (ESI), RFs are governed by efficiency, which favors polar and ionic compounds due to their ability to form charged droplets in the process, while nonpolar s may show suppressed responses. Instrumental conditions further modulate RF variability. Precise control of injection volume is critical in GC, as inconsistencies (e.g., from autosampler variability) can lead to uneven analyte delivery, altering peak areas and thus RF reproducibility by several percent across runs. In GC, column temperature influences peak broadening through changes in volatility and ; elevated temperatures reduce retention times but can distort peak shapes if not optimized, indirectly affecting integrated peak areas used in RF calculations. Sources of RF variability include inherent detector drift and sample matrix interferences. FID detectors exhibit day-to-day signal drift of approximately 1–5% due to factors like flame stability or gas flow fluctuations, necessitating frequent recalibration to maintain accuracy. In complex samples, matrix effects—such as co-eluting interferents competing for in MS or quenching signals in detectors—can alter RFs by up to 50%, particularly in ESI-MS where ion suppression is prevalent. To mitigate these variations, RFs are often determined as averages from multiple replicate runs (e.g., at least six independent analyses over several days) to account for instrumental inconsistencies. Instrument qualification under (GLP) guidelines ensures ongoing performance verification through routine calibration and maintenance protocols. Historically, the limitations of early FID detectors in the , including inconsistent responses to functional groups beyond simple hydrocarbons, drove the development of ECN-based standardization to enable more reliable quantitative analysis.

Analyte Properties

The response factor of an in analytical techniques such as with flame detection (GC-FID) is influenced by its molecular structure, particularly the number of carbon atoms and the presence of functional groups. In GC-FID, the detector response is generally proportional to the effective carbon number, where each carbon atom contributes to production during , leading to higher response factors for hydrocarbons with more carbon atoms. Functional groups can modify this response; for instance, oxygen-containing groups in alcohols or ethers may slightly reduce the response per carbon due to altered pathways, while in chlorinated or brominated compounds typically lower the response factor by 20-50% compared to non-halogenated analogs, attributed to suppressed from electronegative effects. Polarity and volatility of the analyte play critical roles in determining response factors across separation techniques. In (ESI-MS), nonpolar analytes often exhibit lower response factors due to reduced efficiency, as low polarity hinders droplet formation and ion transfer in the process, particularly for non-ionizable nonpolar compounds. Conversely, volatile compounds generally yield higher and more consistent response factors in GC methods, where their ease of and transfer to the detector enhances detection sensitivity, whereas in liquid chromatography (LC), low-volatility analytes perform better due to improved and retention in the mobile phase. Matrix interactions further modulate response factors, especially in . Co-eluting interferents in complex samples can suppress the response factor through ion competition in the ionization source, leading to reduced signal intensity by up to 50% or more in ESI-MS, as matrix components alter charge distribution and yield. This suppression effect is -dependent, with more competitive matrices exacerbating variability for trace-level detections. Representative examples illustrate these property influences. In polycyclic aromatic hydrocarbons (PAHs), alkyl-substituted variants show varying relative response factors (RRFs) due to chain branching; branched alkyl-PAHs often exhibit 10-30% lower RRFs in GC-MS compared to linear counterparts, stemming from differences in ionization efficiency and fragmentation patterns. For pharmaceuticals analyzed by LC-UV, compounds with strong chromophores, such as aromatic rings with conjugated systems in drugs like aspirin or ibuprofen, display higher response factors at typical detection wavelengths (e.g., 254 nm), enabling sensitive detection without calibration for each analog. To estimate response factors without extensive experimentation, quantitative structure-response relationships (QSRR) models have emerged since the early , correlating molecular descriptors like hydrophobicity, polar surface area, and electronic properties with detector responses in chromatography-MS workflows. These predictive approaches, often based on , achieve prediction accuracies within 20% for diverse compound classes, facilitating non-target analysis.

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